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b)\(\frac{x^3-y^3}{3x^2-3xy}=\frac{\left(x-y\right)\left(x^2+xy+y^2\right)}{3x\left(x-y\right)}=\frac{x^2+xy+y^2}{3x}\)
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Bài 2: Rút gọn phân thứcAfrac{10x^2-7+5x-2xy}{1-2x^2+x}Bài 3: Chứng minh rằnga) frac{x^2y+2xy^2+y^3}{2x^2+xy-y^2}frac{xy+y^2}{2x-y}b) frac{x^2+3xy+2y^2}{x^3+2x^2y-xy^2-2y^3}frac{1}{x-y}Bài 4: Quy đồng mẫu thức các phân thức saua) frac{5x}{left(x+3right)^3}&frac{x-4}{3xleft(x+2right)^2}b) frac{x+1}{x-x^2}&frac{x+2}{2x^2+2-4x}
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Bài 2: Rút gọn phân thức
\(A=\frac{10x^2-7+5x-2xy}{1-2x^2+x}\)
Bài 3: Chứng minh rằng
a) \(\frac{x^2y+2xy^2+y^3}{2x^2+xy-y^2}=\frac{xy+y^2}{2x-y}\)
b) \(\frac{x^2+3xy+2y^2}{x^3+2x^2y-xy^2-2y^3}=\frac{1}{x-y}\)
Bài 4: Quy đồng mẫu thức các phân thức sau
a) \(\frac{5x}{\left(x+3\right)^3}\&\frac{x-4}{3x\left(x+2\right)^2}\)
b) \(\frac{x+1}{x-x^2}\&\frac{x+2}{2x^2+2-4x}\)
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,\(\frac{1}{1-x}+\frac{1}{1+x}+\frac{2}{1+x^2}+\frac{4}{1+x^4}+\frac{8}{1+x^8}+\frac{16}{1+x^{16}}\)
\(\frac{x-3}{3xy}\)+ \(\frac{5x+3}{3xy}\)
\(\frac{5x-7}{2x-3}+\frac{4-3x}{2x-3}\)
\(\frac{3x+5}{7x-1}-\frac{6-4x}{7x-1}\)
\(\frac{11x-7}{3-5x}-\frac{6x+4}{5x-3}\)
\(\frac{3}{2x+6}-\frac{x-6}{2x^2+6x}\)
\(\frac{1}{2x-10}+\frac{2x}{3x^2-15x}\)
1,Thực hiện phép tính
a,\(\frac{3}{2x^2+2x}+\frac{2x-1}{x^2-1}-\frac{2}{x}\)
b,\(\frac{3x}{5x+5y}-\frac{x}{10x-10y}\)
c,\(\frac{5x^2-y^2}{xy}-\frac{3x-2y}{y}\)
d,\(\frac{3}{2x+6}-\frac{x-6}{2x^2+6x}\)
7,Thực hiện phép tínha,frac{4x+1}{2}-frac{3x+2}{3} b,frac{x+3}{x^2-1}-frac{1}{x^2+x} c,frac{3}{2x^2+2x}+frac{2x-1}{x^2-1}-frac{1}{2}d,frac{3x}{5x+5y}-frac{x}{10x-10y} e,frac{5x^2-y^2}{xy}-frac{3x-2y}{y} f,frac{3}{2x+6}-frac{x-6}{2x^2+6x}
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7,Thực hiện phép tính
a,\(\frac{4x+1}{2}-\frac{3x+2}{3}\)
b,\(\frac{x+3}{x^2-1}-\frac{1}{x^2+x}\)
c,\(\frac{3}{2x^2+2x}+\frac{2x-1}{x^2-1}-\frac{1}{2}\)
d,\(\frac{3x}{5x+5y}-\frac{x}{10x-10y}\)
e,\(\frac{5x^2-y^2}{xy}-\frac{3x-2y}{y}\)
f,\(\frac{3}{2x+6}-\frac{x-6}{2x^2+6x}\)
giải phương trình sau:
a) \(\frac{3x+2}{3x-2}-\frac{6}{2+3x}=\frac{9x^2}{9x-4}\\\)
b) \(\frac{3}{5x-1}+\frac{2}{3-5x}=\frac{4}{\left(1-5x\right)\left(x-3\right)}\)
c)\(\frac{3}{1-4x}=\frac{2}{4x+1}-\frac{8+6x}{16x^2-1}\)
d) \(5+\frac{76}{x^2-16}=\frac{2x-1}{x+4}-\frac{3x-1}{4-x}\)
a,frac{3x^2-6xy+3y^2}{5x^2-5xy+5y^2}:frac{10x-10y}{x^3+y^3}b,(frac{x+2}{x+1}-frac{2x}{x-1}).frac{3x+3}{x}+frac{4x^2+x+7}{x^2-x}c,frac{2}{xy}:left(frac{1}{x}-frac{1}{y}right)-frac{x^2-y^2}{left(x-yright)^2}d,frac{frac{x-y}{x+y}-frac{x+y}{x-y}}{1-frac{x^2}{x^2+y^2}}e,left(frac{1}{x+1}-frac{3}{x^3+1}+frac{3}{x^2-x+1}right).frac{3x^2-3x+3}{left(x+1right)left(x+2right)}+frac{2x-2}{x^2+2x}
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\(a,\frac{3x^2-6xy+3y^2}{5x^2-5xy+5y^2}:\frac{10x-10y}{x^3+y^3}\)
\(b,(\frac{x+2}{x+1}-\frac{2x}{x-1}).\frac{3x+3}{x}+\frac{4x^2+x+7}{x^2-x}\)
\(c,\frac{2}{xy}:\left(\frac{1}{x}-\frac{1}{y}\right)-\frac{x^2-y^2}{\left(x-y\right)^2}\)
\(d,\frac{\frac{x-y}{x+y}-\frac{x+y}{x-y}}{1-\frac{x^2}{x^2+y^2}}\)
\(e,\left(\frac{1}{x+1}-\frac{3}{x^3+1}+\frac{3}{x^2-x+1}\right).\frac{3x^2-3x+3}{\left(x+1\right)\left(x+2\right)}+\frac{2x-2}{x^2+2x}\)
Ai giúp vs !!!
\(a.\frac{3x-7}{5}=\frac{2x-1}{3}\\ b.\frac{4x-7}{12}-x=\frac{3x}{8}\\ c.\frac{x-2009}{1234}+\frac{x-2009}{5678}-\frac{x-2009}{197}=0\\ d.\frac{5x-8}{3}=\frac{1-3x}{2}\\ e.\frac{x-5}{6}-\frac{x-9}{4}=\frac{5x-3}{8}+2\\ f.\frac{x-1}{\frac{2}{5}}-3-\frac{3x-2}{\frac{5}{4}}-2=1\)
Rút gọn các phân thức:a)frac{x^4-4x^2+3}{x^4+6x^2-7}b)frac{x^4+x^3-x-1}{x^4+x^3+2x^2+x+1}c)frac{x^3+3x^2-4}{x^3-3x+2}d)frac{3x^3-7x^2+5x-1}{2x^3-x^2-4x+3}e)frac{left(x-yright)^3-3xyleft(x+yright)+y^3}{x-6y}f)frac{x^2+y^2+z^2-2xy+2xz-2yz}{x^2-2xy+y^2-z^2}
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Rút gọn các phân thức:
a)\(\frac{x^4-4x^2+3}{x^4+6x^2-7}\)
b)\(\frac{x^4+x^3-x-1}{x^4+x^3+2x^2+x+1}\)
c)\(\frac{x^3+3x^2-4}{x^3-3x+2}\)
d)\(\frac{3x^3-7x^2+5x-1}{2x^3-x^2-4x+3}\)
e)\(\frac{\left(x-y\right)^3-3xy\left(x+y\right)+y^3}{x-6y}\)
f)\(\frac{x^2+y^2+z^2-2xy+2xz-2yz}{x^2-2xy+y^2-z^2}\)