Question

[Ninh Thanh Tú Anh]

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) \(\frac{x+1}{x-x^2}\&\frac{x+2}{2x^2+2-4x}\)

Answer 1

[Kiệt Nguyễn]

Ta có: \(\frac{x^2y+2xy^2+y^3}{2x^2+xy-y^2}\)

\(=\frac{x^2y+xy^2+xy^2+y^3}{2x^2+2xy-xy-y^2}\)

\(=\frac{xy\left(x+y\right)+y^2\left(x+y\right)}{2x\left(x+y\right)-y\left(x+y\right)}\)

\(=\frac{\left(x+y\right)\left(xy+y^2\right)}{\left(2x-y\right)\left(x+y\right)}=\frac{xy+y^2}{2x-y}\left(đpcm\right)\)

Answer 2

[Kiệt Nguyễn]

Ta có: \(\frac{x^2+3xy+2y^2}{x^3+2x^2y-xy^2-2y^3}\)

\(=\frac{x^2+xy+2xy+2y^2}{x^2\left(x+2y\right)-y^2\left(x+2y\right)}\)

\(=\frac{x\left(x+y\right)+2y\left(x+y\right)}{\left(x^2-y^2\right)\left(x+2y\right)}\)

\(=\frac{\left(x+2y\right)\left(x+y\right)}{\left(x+y\right)\left(x-y\right)\left(x+2y\right)}=\frac{1}{x-y}\left(đpcm\right)\)