Question

Rút gọn phân thức

\(\frac{x^4-y^4}{y^3-x^3}\)

Answer 1

\(\frac{x^4-y^4}{y^3-x^3}\)

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

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

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

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