Thực hiện phép tính
\(\frac{2x+y}{2x^2-xy}+\frac{8y}{y^2-4x^2}+\frac{2x-y}{2x^2+xy}\)
Những câu hỏi liên quan
thực hiện phép tính \(\frac{2x+y}{2x^2-xy}+\frac{16}{y^2-4x^2}+\frac{2-y}{2x^2+xy}\)
CM tổng sau :
\(\frac{2x+y}{2x^2-xy}+\frac{8y}{y^2-4x^2}+\frac{2x-y}{2x^2+xy}=\frac{2.\left(2x-y\right)}{x.\left(2x+y\right)}.\)
Thực hiện phép tính sau:
\(\frac{xy}{x-y}-\frac{2x^2}{y-2x}\)
\(\dfrac{xy}{x-y}-\dfrac{2x^2}{y-2x}\)
\(=\dfrac{xy}{x-y}+\dfrac{2x^2}{2x-y}\)
\(=\dfrac{xy\left(2x-y\right)+2x^2\left(x-y\right)}{\left(x-y\right)\left(2x-y\right)}\)
\(=\dfrac{2x^2y-xy^2+2x^3-2x^2y}{\left(x-y\right)\left(2x-y\right)}\)
\(=\dfrac{2x^3-xy^2}{\left(x-y\right)\left(2x-y\right)}=\dfrac{x\left(2x^2-y^2\right)}{\left(x-y\right)\left(2x-y\right)}\)
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cộng trừ các phân thức
\(\frac{2x+y}{2x^2-xy}+\frac{8y}{y^2-4x^2}+\frac{2x-y}{2x^2+xy}\)
\(\frac{2x+y}{2x^2-xy}+\frac{8y}{y^2-4x^2}+\frac{2x-y}{2x^2+xy}\)
\(=\frac{2x+y}{x\left(2x-y\right)}-\frac{8y}{\left(2x-y\right)\left(2x+y\right)}+\frac{2x-y}{x\left(2x+y\right)}\)
\(=\frac{\left(2x+y\right)^2-8xy+\left(2x-y\right)^2}{x\left(2x-y\right)\left(2x+y\right)}=\frac{4x^2+4xy+y^2-8xy+4x^2-4xy+y^2}{x\left(2x-y\right)\left(2x+y\right)}\)
\(=\frac{8x^2-8xy+2y^2}{x\left(2x-y\right)\left(2x+y\right)}=\frac{2\left(4x^2-4xy+y^2\right)}{x\left(2x-y\right)\left(2x+y\right)}\)
\(=\frac{2\left(2x-y\right)^2}{x\left(2x-y\right)\left(2x+y\right)}=\frac{2\left(2x-y\right)}{x\left(2x+y\right)}\)
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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
\(\frac{y}{2x^2-xy}\)\(+\)\(\frac{4x}{y^2-2xy}\)
\(\frac{y}{2x^2-xy}+\frac{4x}{y^2-2xy}=0\)
<=>\(\frac{y}{x\left(2x-y\right)}-\frac{4x}{y\left(2x-y\right)}=0\)
<=>\(\frac{y^2}{xy\left(2x-y\right)}-\frac{4x^2}{xy\left(2x-y\right)}=0\)
=>y2-(2x)2=0
<=>(y-2x)(y+2x)=0
<=>y-2x=0 hoặc y+2x=0
M chỉ làm đc đến đó thôi!!!!!
5,Thực hiện phép tính
1,\(\frac{3}{2x+6}-\frac{x-6}{2x^2+6x}\)
2,\(\frac{1}{1-x}+\frac{2x}{x^2-1}\)
3,\(\frac{1}{xy-x^2}-\frac{1}{y^2-xy}\)
4,\(\frac{5x+10}{4x-8}.\frac{4-2x}{x+2}\)
5,\(\frac{1-4x^2}{x^2+4x}:\frac{2-4x}{3x}\)
1,\(\frac{3}{2x+6}-\frac{x-6}{x\left(2x+6\right)}\)
=\(\frac{3x}{x\left(2x+6\right)}+\frac{x-6}{x\left(2x+6\right)}\)
=\(\frac{3x+x-6}{x\left(2x+6\right)}\)=\(\frac{4x-6}{x\left(2x+6\right)}=\frac{2\left(2x-3\right)}{x\left(2x+6\right)}\)
2, \(\frac{1}{1-x}-\frac{2x}{1-x^2}\)=\(\frac{1+x}{\left(1-x\right)\left(1+x\right)}+\frac{2x}{\left(1-x\right)\left(1+x\right)}\)=\(\frac{1+x+2x}{\left(1-x\right)\left(1+x\right)}=\frac{3x+1}{\left(1-x\right)\left(1+x\right)}\)
3,1/x(y-x)-1/y(y-x)=y/xy(y-x)-x/xy(y-x)=(y-x)/xy(x-y)=1/xy
Tính:\(A=\frac{2x+y}{2x^2-xy}+\frac{16x}{y^2-4x}\)\(+\frac{2x-y}{2x^2+xy}\)
kết quả này có đúng không thì mình chưa chắc bạn nhé : \(\frac{4x+16}{y^2-4x}\)
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Thực hiện phép tính:a) frac{1}{x}-frac{1}{x+1}b)frac{1}{xy-x^2}-frac{1}{y^2-xy}c) frac{9x-3}{4x-1}-frac{3x}{1-4x}d) frac{2x-1}{x}-frac{2x+5}{3x-4x^2}+frac{2x^2+x+3}{3x-4x^2}e) frac{x}{2x+1}+frac{1}{4x^2-1}-frac{x-2}{2x-1}giúp mình với mình cần gấp ! Help me )
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Thực hiện phép tính:
a) \(\frac{1}{x}-\frac{1}{x+1}\)
b)\(\frac{1}{xy-x^2}-\frac{1}{y^2-xy}\)
c) \(\frac{9x-3}{4x-1}-\frac{3x}{1-4x}\)
d) \(\frac{2x-1}{x}-\frac{2x+5}{3x-4x^2}+\frac{2x^2+x+3}{3x-4x^2}\)
e) \(\frac{x}{2x+1}+\frac{1}{4x^2-1}-\frac{x-2}{2x-1}\)
giúp mình với mình cần gấp ! Help me ===)
\(\frac{1}{x}-\frac{1}{x+1}=\frac{x+1-x}{x\left(x+1\right)}=\frac{1}{x^2+x}\)
b, \(\frac{1}{xy-x^2}-\frac{1}{y^2-xy}=\frac{y^2-xy-xy+x^2}{\left(xy-x^2\right)\left(y^2-xy\right)}=\frac{x^2+y^2}{xy^3-xyxy-xyxy+x^3y}\)Tu rut gon tiep
c, tt
d, cx r
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a) \(\frac{1}{x}-\frac{1}{x+1}=\frac{x+1}{x\left(x+1\right)}-\frac{x}{x\left(x+1\right)}\)
\(=\frac{x+1-x}{x\left(x+1\right)}=\frac{1}{x\left(x+1\right)}\)
b) \(\frac{1}{xy-x^2}-\frac{1}{y^2-xy}=\frac{1}{x\left(y-x\right)}-\frac{1}{y\left(y-x\right)}\)
\(=\frac{y}{xy\left(y-x\right)}-\frac{x}{xy\left(y-x\right)}=\frac{y-x}{xy\left(y-x\right)}=\frac{1}{xy}\)
c) \(\frac{9x-3}{4x-1}-\frac{3x}{1-4x}=\frac{9x-3}{4x-1}+\frac{3x}{4x-1}\)
\(=\frac{9x-3+3x}{4x-1}=\frac{6x-3}{4x-1}\)
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\(a,\frac{1}{x}-\frac{1}{x+1}\)
\(=\frac{x+1}{x\left(x+1\right)}-\frac{x}{x\left(x+1\right)}=\frac{x+1-x}{x\left(x+1\right)}\)
\(=\frac{1}{x\left(x+1\right)}\)
\(b,\frac{1}{xy-x^2}-\frac{1}{y^2-xy}\)
\(=\frac{1}{x\left(y-x\right)}-\frac{1}{y\left(y-x\right)}\)
\(=\frac{y}{xy\left(y-x\right)}-\frac{x}{xy\left(y-x\right)}=\frac{x-y}{xy\left(x-y\right)}=\frac{1}{xy}\)
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