Thực hiện phép tính
a, (\(\frac{3}{y-3}-\frac{2}{y-y^2}+\frac{y}{y+3}\)) : \(\frac{2y}{y+3}\) b,(\(\frac{3x}{1-2x}+\frac{x}{2x+1}\)) : \(\frac{4\left(x+1\right)}{1-4x+4x^2}\)
Những câu hỏi liên quan
Bài 1 :Thực hiện phép tính
a, frac{2x}{x^2+2xy}+frac{y}{xy-2y^2}+frac{4}{x^2-4y^2}
bfrac{1}{x-y}+frac{3xy}{y^3-x^3}+frac{x-y}{x^2+xy+y^2}
c, frac{xy}{2x-y}-frac{x^2-1}{y-2x}
d,frac{2left(x+yright)left(x-yright)}{x}-frac{-2y^2}{x}
Bài 2: Thực hiện phép tính
a,frac{4x+1}{2}-frac{3x+2}{3}
b,frac{x+3}{x}-frac{x}{x-3}+frac{9}{x^2-3x}
c,frac{x+3}{x^2+1}-frac{1}{x^2+2}
e,frac{3}{2x^2+2x}+frac{2x-1}{x^2-1}-frac{2}{x}
d,frac{1}{3x-2}-frac{4}{3x+2}-frac{-10x+8}{9x^2-4}
f,frac{3x}{5x+5y}-frac{x}...
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Bài 1 :Thực hiện phép tính
a, \(\frac{2x}{x^2+2xy}+\frac{y}{xy-2y^2}+\frac{4}{x^2-4y^2}\)
b\(\frac{1}{x-y}+\frac{3xy}{y^3-x^3}+\frac{x-y}{x^2+xy+y^2}\)
c, \(\frac{xy}{2x-y}-\frac{x^2-1}{y-2x}\)
d,\(\frac{2\left(x+y\right)\left(x-y\right)}{x}-\frac{-2y^2}{x}\)
Bài 2: Thực hiện phép tính
a,\(\frac{4x+1}{2}-\frac{3x+2}{3}\)
b,\(\frac{x+3}{x}-\frac{x}{x-3}+\frac{9}{x^2-3x}\)
c,\(\frac{x+3}{x^2+1}-\frac{1}{x^2+2}\)
e,\(\frac{3}{2x^2+2x}+\frac{2x-1}{x^2-1}-\frac{2}{x}\)
d,\(\frac{1}{3x-2}-\frac{4}{3x+2}-\frac{-10x+8}{9x^2-4}\)
f,\(\frac{3x}{5x+5y}-\frac{x}{10x-10y}\)
Bài 1:
a) Ta có: \(\frac{2x}{x^2+2xy}+\frac{y}{xy-2y^2}+\frac{4}{x^2-4y^2}\)
\(=\frac{2x}{x\left(x+2y\right)}+\frac{y}{y\left(x-2y\right)}+\frac{4}{\left(x-2y\right)\left(x+2y\right)}\)
\(=\frac{2}{x+2y}+\frac{y}{x-2y}+\frac{4}{\left(x-2y\right)\left(x+2y\right)}\)
\(=\frac{2\left(x-2y\right)}{\left(x+2y\right)\left(x-2y\right)}+\frac{y\left(x+2y\right)}{\left(x-2y\right)\left(x+2y\right)}+\frac{4}{\left(x-2y\right)\left(x+2y\right)}\)
\(=\frac{2x-4y+xy+2y^2+4}{\left(x-2y\right)\cdot\left(x+2y\right)}\)
b) Ta có: \(\frac{1}{x-y}+\frac{3xy}{y^3-x^3}+\frac{x-y}{x^2+xy+y^2}\)
\(=\frac{x^2+xy+y^2}{\left(x-y\right)\left(x^2+xy+y^2\right)}-\frac{3xy}{\left(x-y\right)\left(x^2+xy+y^2\right)}+\frac{\left(x-y\right)^2}{\left(x-y\right)\left(x^2+xy+y^2\right)}\)
\(=\frac{x^2+xy+y^2-3xy+x^2-2xy+y^2}{\left(x-y\right)\left(x^2+xy+y^2\right)}\)
\(=\frac{2x^2-4xy+2y^2}{\left(x-y\right)\left(x^2+xy+y^2\right)}\)
\(=\frac{2\left(x^2-2xy+y^2\right)}{\left(x-y\right)\left(x^2+xy+y^2\right)}\)
\(=\frac{2\left(x-y\right)^2}{\left(x-y\right)\left(x^2+xy+y^2\right)}\)
\(=\frac{2x-2y}{x^2+xy+y^2}\)
c) Ta có: \(\frac{xy}{2x-y}-\frac{x^2-1}{y-2x}\)
\(=\frac{xy}{2x-y}+\frac{x^2-1}{2x-y}\)
\(=\frac{x^2+xy-1}{2x-y}\)
d) Ta có: \(\frac{2\left(x+y\right)\left(x-y\right)}{x}-\frac{-2y^2}{x}\)
\(=\frac{2\left(x^2-y^2\right)+2y^2}{x}\)
\(=\frac{2x^2-2y^2+2y^2}{x}\)
\(=\frac{2x^2}{x}=2x\)
Bài 2:
a) Ta có: \(\frac{4x+1}{2}-\frac{3x+2}{3}\)
\(=\frac{3\left(4x+1\right)}{6}-\frac{2\left(3x+2\right)}{6}\)
\(=\frac{12x+3-6x-4}{6}\)
\(=\frac{6x-1}{6}\)
b) Ta có: \(\frac{x+3}{x}-\frac{x}{x-3}+\frac{9}{x^2-3x}\)
\(=\frac{\left(x+3\right)\left(x-3\right)}{x\left(x-3\right)}-\frac{x^2}{x\left(x-3\right)}+\frac{9}{x\left(x-3\right)}\)
\(=\frac{x^2-9-x^2+9}{x\left(x-3\right)}=\frac{0}{x\left(x-3\right)}=0\)
c) Ta có: \(\frac{x+3}{x^2+1}-\frac{1}{x^2+2}\)
\(=\frac{\left(x+3\right)\left(x^2+2\right)}{\left(x^2+1\right)\left(x^2+2\right)}-\frac{x^2+1}{\left(x^2+2\right)\left(x^2+1\right)}\)
\(=\frac{x^3+2x+3x^2+6-x^2-1}{\left(x^2+1\right)\left(x^2+2\right)}\)
\(=\frac{x^3+2x^2+2x+5}{\left(x^2+1\right)\left(x^2+2\right)}\)
e) Ta có: \(\frac{3}{2x^2+2x}+\frac{2x-1}{x^2-1}-\frac{2}{x}\)
\(=\frac{3}{2x\left(x+1\right)}+\frac{2x-1}{\left(x+1\right)\left(x-1\right)}-\frac{2}{x}\)
\(=\frac{3\left(x-1\right)}{2x\left(x+1\right)\left(x-1\right)}+\frac{2x\left(2x-1\right)}{2x\left(x+1\right)\left(x-1\right)}-\frac{2\cdot2\cdot\left(x+1\right)\left(x-1\right)}{2x\left(x+1\right)\left(x-1\right)}\)
\(=\frac{3x-3+4x^2-2x-4\left(x^2-1\right)}{2x\left(x+1\right)\left(x-1\right)}\)
\(=\frac{4x^2+x-3-4x^2+4}{2x\left(x+1\right)\left(x-1\right)}\)
\(=\frac{x+1}{2x\left(x+1\right)\left(x-1\right)}=\frac{1}{2x\left(x-1\right)}\)
d) Ta có: \(\frac{1}{3x-2}-\frac{4}{3x+2}-\frac{-10x+8}{9x^2-4}\)
\(=\frac{3x+2}{\left(3x-2\right)\left(3x+2\right)}-\frac{4\left(3x-2\right)}{\left(3x+2\right)\left(3x-2\right)}-\frac{-10x+8}{\left(3x-2\right)\left(3x+2\right)}\)
\(=\frac{3x+2-12x+8+10x-8}{\left(3x-2\right)\left(3x+2\right)}\)
\(=\frac{x+2}{\left(3x-2\right)\left(3x+2\right)}\)
f) Ta có: \(\frac{3x}{5x+5y}-\frac{x}{10x-10y}\)
\(=\frac{3x}{5\left(x+y\right)}-\frac{x}{10\left(x-y\right)}\)
\(=\frac{3x\cdot2\cdot\left(x-y\right)}{10\left(x+y\right)\left(x-y\right)}-\frac{x\cdot\left(x+y\right)}{10\left(x-y\right)\left(x+y\right)}\)
\(=\frac{6x^2-6xy-x^2-xy}{10\left(x-y\right)\left(x+y\right)}\)
\(=\frac{5x^2-7xy}{10\left(x-y\right)\left(x+y\right)}\)
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8,Thực hiện phép tínha,frac{5x^2-y^2}{xy}-frac{3x-2y}{y}b,frac{3}{2x+6}-frac{x-6}{2x^2+6x}c,frac{2x}{x^2+2xy}+frac{y}{xy-2y^2}+frac{4}{x^2-4y^2} d,frac{1}{x-y}+frac{3xy}{y^3-x^3}+frac{x-y}{x^2+xy+y^2} e,frac{2x+y}{2x^2-xy}+frac{16x}{y^2-4x^2}+frac{2x-y}{2x^2+xy} f,frac{1}{1-x}+frac{1}{1+x}+frac{2}{1+x^2}+frac{4}{1+x^4}+frac{8}{1+x^8}+frac{16}{1+x^{16}}
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8,Thực hiện phép tính
a,\(\frac{5x^2-y^2}{xy}-\frac{3x-2y}{y}\)
b,\(\frac{3}{2x+6}-\frac{x-6}{2x^2+6x}\)
c,\(\frac{2x}{x^2+2xy}+\frac{y}{xy-2y^2}+\frac{4}{x^2-4y^2}\)
d,\(\frac{1}{x-y}+\frac{3xy}{y^3-x^3}+\frac{x-y}{x^2+xy+y^2}\)
e,\(\frac{2x+y}{2x^2-xy}+\frac{16x}{y^2-4x^2}+\frac{2x-y}{2x^2+xy}\)
f,\(\frac{1}{1-x}+\frac{1}{1+x}+\frac{2}{1+x^2}+\frac{4}{1+x^4}+\frac{8}{1+x^8}+\frac{16}{1+x^{16}}\)
Thực hiện phép tính:
a. 2x(x + y) - y(y + 2x)
b. \(\frac{4x+3y}{7x^2y}-\frac{3x+3y}{7x^2y}\)
c.\(\frac{x^3-4x^2}{x^3-1}+\frac{2}{x^2+x+1}+\frac{1}{x-1}\)
ai giúp minh với!! tối mai mình phải trả đề cương rồi!!
a. 2x(x + y) - y(y + 2x) = 2x2 + 2xy - y2 - 2xy = 2x2 - y2
b.\(\frac{4x+3y}{7x^2y}-\frac{3x+3y}{7x^2y}=\frac{4x+3y-3x-3y}{7x^2y}=\frac{x}{7x^2y}=\frac{1}{7xy}\)
Phần c nản quá.
Thực hiện phép tính:
a. 2x(x + y) - y(y + 2x)
b. \(\frac{4x+3y}{7x^2y}-\frac{3x+3y}{7x^2y}\)
c.\(\frac{x^3-4x^2}{x^3-1}+\frac{2}{x^2+x+1}+\frac{1}{x-1}\)
ai giúp minh với!! tối mai mình phải trả đề cương rồi!!
a) 2x(x + y) - y(y + 2x)
= 2x2 + 2xy - y2 - 2xy
= 2x2 - y2
b) \(\frac{4x+3y}{7x^2y}-\frac{3x+3y}{7x^2y}=\frac{4x+3y-3x-3y}{7x^2y}=\frac{x}{7x^2y}=\frac{1}{7xy}\)
c) \(\frac{x^3-4x^2}{x^3-1}+\frac{2}{x^2+x+1}+\frac{1}{x-1}\)
= \(\frac{x^3-4x^2}{\left(x-1\right)\left(x^2+x+1\right)}+\frac{2\left(x-1\right)}{\left(x^2+x+1\right)\left(x-1\right)}+\frac{x^2+x+1}{\left(x^2+x+1\right)\left(x-1\right)}\)
= \(\frac{x^3-4x^2+2x-2+x^2+x+1}{\left(x^2+x+1\right)\left(x-1\right)}=\frac{x^3-3x^2+3x-1}{\left(x^2+x+1\right)\left(x-1\right)}=\frac{\left(x-1\right)^3}{\left(x^2+x+1\right)\left(x-1\right)}\)
\(=\frac{\left(x-1\right)^2}{x^2+x+1}\)
1/Thực hiện phép tính :a)left(frac{1}{2}a^2x^4+frac{4}{3}ax^3-frac{2}{3}ax^2right): left(-frac{2}{3}ax^2right)b) 4left(frac{3}{4}x-1right)+left(12x^2-3xright):left(-3xright)-left(2x+1right)2/Rút gọn biểu thức:((x3+y3)-2(x2-y2)+3(x+y)2) : (x+y)3/Chia các đa thức:a)(3x4-2x3-2x2+4x-8):(x2-2)b)(2x3-26x-24):(x2+4x+3)c)(x3-7x+6):(x+3)
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1/Thực hiện phép tính :
a)\(\left(\frac{1}{2}a^2x^4+\frac{4}{3}ax^3-\frac{2}{3}ax^2\right)\): \(\left(-\frac{2}{3}ax^2\right)\)
b) \(4\left(\frac{3}{4}x-1\right)+\left(12x^2-3x\right):\left(-3x\right)-\left(2x+1\right)\)
2/Rút gọn biểu thức:
((x3+y3)-2(x2-y2)+3(x+y)2) : (x+y)
3/Chia các đa thức:
a)(3x4-2x3-2x2+4x-8):(x2-2)
b)(2x3-26x-24):(x2+4x+3)
c)(x3-7x+6):(x+3)
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55555555555555555
666666666666666666666666666
88888888888888888888
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Tính
a, \(\frac{1}{\left(y-1\right)\left(y-2\right)}+\frac{2}{\left(2-y\right)\left(3y-y\right)}+\frac{3}{\left(1-y\right)\left(y-3\right)}\)
b, \(\frac{x^2}{x+1}+\frac{2x}{x^2-1}-\frac{1}{1-x}+1\)
c, \(\frac{1}{x^2+3x+2}-\frac{2x}{x^2+4x^2+4x}+\frac{1}{x^2+5x+6}\)
1)Thực hiện phép tính
a)\(\frac{y}{2x^2-xy}+\frac{4x}{y^2-2xy}\)
b)\(\frac{1}{x+2}+\frac{3}{x^2-4}+\frac{x-14}{\left(x^2+4x+4\right)\left(x-2\right)}\)
a) ĐKXĐ: \(x;y\ne0,x\ne\frac{y}{2},y\ne\frac{x}{2}\)
\(\frac{y}{2x^2-xy}+\frac{4x}{y^2-2xy}=\frac{y}{x\left(2x-y\right)}-\frac{4x}{y\left(2x-y\right)}\)\(=\frac{y^2-4x^2}{xy\left(2x-y\right)}=\frac{\left(y-2x\right)\left(y+2x\right)}{xy\left(2x-y\right)}\)
\(=\frac{-\left(y+2x\right)}{xy}\)
b) ĐKXĐ: \(x\ne2;x\ne-2\)
\(\frac{1}{x+2}+\frac{3}{x^2-4}+\frac{x-14}{\left(x^2+4x+4\right)\left(x-2\right)}\)\(=\frac{1}{x+2}+\frac{3}{\left(x-2\right)\left(x+2\right)}+\frac{x-14}{\left(x+2\right)^2\left(x-2\right)}\)
\(=\frac{\left(x-2\right)\left(x+2\right)+3\left(x+2\right)+x-14}{\left(x+2\right)^2\left(x-2\right)}\)\(=\frac{x^2-4+3x+6+x-14}{\left(x+2\right)^2\left(x-2\right)}\)\(=\frac{x^2+4x-12}{\left(x+2\right)^2\left(x-2\right)}=\frac{\left(x^2+4x+4\right)-16}{\left(x+2\right)^2\left(x-2\right)}\)\(=\frac{\left(x+2\right)^2-16}{\left(x+2\right)^2\left(x-2\right)}=\frac{\left(x+2-4\right)\left(x+2+4\right)}{\left(x+2\right)^2\left(x-2\right)}\)\(=\frac{\left(x-2\right)\left(x+6\right)}{\left(x+2\right)^2\left(x-2\right)}=\frac{x+6}{\left(x+2\right)^2}\)
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bài 4 tính
a, frac{2x^2-10xy}{2xy}+frac{5y-x}{y}
b, frac{2}{x+y}+frac{1}{x-y}+frac{3x}{x^2-y^2}
c, x+y+frac{x^2+y^2}{x+y}
bài 2 .dùng quy tắc biến đổi dấu để tìm MTC rồi thực hiện phếp tính
1a, frac{4}{x+2}+frac{3x-2}{x-2}+frac{5x-6}{4-x^2}
b,frac{1-3x}{2x}+frac{3x-2}{2x-1}+frac{3x-2}{2x-4x^2}
c. frac{x^2+2}{x^3-1}+frac{2}{x^2+x+1}+frac{1}{1-x}
d, frac{2x+y}{2x^2-xy}+frac{16x}{y^2-4x^2}+frac{2x-y}{2x^2+xy}
e,frac{8}{left(x^2+3right)left(x^2-1right)}+frac{2}{x^2+3}+frac{1}{x+1}
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bài 4 tính
a, \(\frac{2x^2-10xy}{2xy}\)+\(\frac{5y-x}{y}\)
b, \(\frac{2}{x+y}+\frac{1}{x-y}+\frac{3x}{x^2-y^2}\)
c, x+y+\(\frac{x^2+y^2}{x+y}\)
bài 2 .dùng quy tắc biến đổi dấu để tìm MTC rồi thực hiện phếp tính
1a, \(\frac{4}{x+2}+\frac{3x-2}{x-2}+\frac{5x-6}{4-x^2}\)
b,\(\frac{1-3x}{2x}+\frac{3x-2}{2x-1}+\frac{3x-2}{2x-4x^2}\)
c. \(\frac{x^2+2}{x^3-1}+\frac{2}{x^2+x+1}+\frac{1}{1-x}\)
d, \(\frac{2x+y}{2x^2-xy}+\frac{16x}{y^2-4x^2}+\frac{2x-y}{2x^2+xy}\)
e,\(\frac{8}{\left(x^2+3\right)\left(x^2-1\right)}+\frac{2}{x^2+3}+\frac{1}{x+1}\)
Bài 4:
a) \(\frac{2x^2-10xy}{2xy}+\frac{5y-x}{y}\)
\(=\frac{y.\left(2x^2-10xy\right)}{2xy.y}+\frac{2xy.\left(5y-x\right)}{2xy.y}\)
\(=\frac{2x^2y-10xy^2}{2xy^2}+\frac{10xy^2-2x^2y}{2xy^2}\)
\(=\frac{2x^2y-10xy^2+10xy^2-2x^2y}{2xy^2}\)
\(=\frac{0}{2xy^2}\)
\(=0.\)
b) \(\frac{2}{x+y}+\frac{1}{x-y}+\frac{3x}{x^2-y^2}\)
\(=\frac{2}{x+y}+\frac{1}{x-y}+\frac{3x}{\left(x-y\right).\left(x+y\right)}\)
\(=\frac{2.\left(x-y\right)}{\left(x-y\right).\left(x+y\right)}+\frac{1.\left(x+y\right)}{\left(x-y\right).\left(x+y\right)}+\frac{3x}{\left(x-y\right).\left(x+y\right)}\)
\(=\frac{2x-2y}{\left(x-y\right).\left(x+y\right)}+\frac{x+y}{\left(x-y\right).\left(x+y\right)}+\frac{3x}{\left(x-y\right).\left(x+y\right)}\)
\(=\frac{2x-2y+x+y+3x}{\left(x-y\right).\left(x+y\right)}\)
\(=\frac{6x-y}{\left(x-y\right).\left(x+y\right)}\)
c) \(x+y+\frac{x^2+y^2}{x+y}\)
\(=\frac{x+y}{1}+\frac{x^2+y^2}{x+y}\)
\(=\frac{\left(x+y\right).\left(x+y\right)}{x+y}+\frac{x^2+y^2}{x+y}\)
\(=\frac{\left(x+y\right)^2}{x+y}+\frac{x^2+y^2}{x+y}\)
\(=\frac{x^2+2xy+y^2}{x+y}+\frac{x^2+y^2}{x+y}\)
\(=\frac{x^2+2xy+y^2+x^2+y^2}{x+y}\)
\(=\frac{2x^2+2xy+2y^2}{x+y}.\)
Chúc bạn học tốt!
2) Giải phương trìnha) frac{x+1}{x-2}+frac{x-1}{x+2}frac{2left(x^2+2right)}{x^2-4}b) left(2x+3right).left(frac{3x+8}{2-7x}+1right)left(x-5right).left(frac{3x+8}{2-7x}+1right)3) Rút gọna) frac{2x-1}{x^3+1}+frac{2x}{x^2-x+1}+frac{-x}{x+1}+2b) frac{x+1}{2x-2}+frac{x^2+3}{2-2x^2}+frac{1}{1-x}-1,5c) left(frac{x^2}{x^3-4x}-frac{6}{3x-6}+frac{1}{x+2}right).frac{x+2}{6}d) left(frac{x}{xy-y^2}+frac{2x-y}{xy-x^2}right):frac{x^2-2xy+y^2}{x^2y-xy^2}e) [frac{1}{left(2x-yright)^2}+frac{2}{4x^2-y^2}-frac{1}{le...
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2) Giải phương trình
a) \(\frac{x+1}{x-2}+\frac{x-1}{x+2}=\frac{2\left(x^2+2\right)}{x^2-4}\)
b) \(\left(2x+3\right).\left(\frac{3x+8}{2-7x}+1\right)=\left(x-5\right).\left(\frac{3x+8}{2-7x}+1\right)\)
3) Rút gọn
a) \(\frac{2x-1}{x^3+1}+\frac{2x}{x^2-x+1}+\frac{-x}{x+1}+2\)
b) \(\frac{x+1}{2x-2}+\frac{x^2+3}{2-2x^2}+\frac{1}{1-x}-1,5\)
c) \(\left(\frac{x^2}{x^3-4x}-\frac{6}{3x-6}+\frac{1}{x+2}\right).\frac{x+2}{6}\)
d) \(\left(\frac{x}{xy-y^2}+\frac{2x-y}{xy-x^2}\right):\frac{x^2-2xy+y^2}{x^2y-xy^2}\)
e) \([\frac{1}{\left(2x-y\right)^2}+\frac{2}{4x^2-y^2}-\frac{1}{\left(2x+y\right)^2}].\frac{x^2+4xy+y^2}{16x}\)
Mn giúp mik vs mik đang cần gấp
\(a,\frac{x+1}{x-2}+\frac{x-1}{x+2}=\frac{2\left(x^2+2\right)}{x^2-4}\)\(\Leftrightarrow\frac{x^2+3x+2+x^2-3x+2}{x^2-4}=\frac{2\left(x^2+2\right)}{x^2-4}\)
\(\Leftrightarrow2\left(x^2+2\right)=2\left(x^2+2\right)\)(luôn đúng)
Vậy pt có vô số nghiệm
\(b,\Leftrightarrow\left(2x+3\right)\left(\frac{3x+8}{2-7x}+1\right)=\left(x-5\right)\left(\frac{3x+8}{2-7x}+1\right)\)
\(\Leftrightarrow\left(\frac{3x+8}{2-7x}+1\right)\left(2x+3-x+5\right)=0\)\(\Leftrightarrow\left(\frac{-4x+10}{2-7x}\right)\left(x+8\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}-4x+10=0\\x+8=0\end{cases}\Rightarrow}\orbr{\begin{cases}x=\frac{5}{2}\\x=-8\end{cases}}\)
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