Question

Rút gọn :

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

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Answer 1

Rút gọn :
b ) \(\frac{x^2+3xy+2y^2}{x^2+2x^2y-xy^2-2y^2}\)

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

\(=\frac{x\left(x+4\right)+2y\left(x+y\right)}{x\left(x^2-y^2\right)+2y\left(x^2-y^2\right)}\)

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

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

\(=\frac{1}{x-y}\)