Question

Chứng minh: (\(\frac{b}{a^2-ab}\)-\(\frac{a}{ab-b^2}\)).(\(\frac{a^2b-ab^2}{a^2-b^2}\))=-1

Answer 1

mọi người giúp em với ạ, chiều nay em thi rồi

Answer 2

Ta có : VT = \(\left(\frac{b}{a\left(a-b\right)}-\frac{a}{b\left(a-b\right)}\right)\cdot\left(\frac{ab\left(a-b\right)}{\left(a-b\right)\left(a+b\right)}\right)\)

\(=\left(\frac{b^2-a^2}{ab\left(a-b\right)}\right).\left(\frac{ab\left(a-b\right)}{\left(a-b\right)\left(a+b\right)}\right)\)

\(=\frac{\left(b-a\right)\left(b+a\right)}{ab\left(a-b\right)}\cdot\frac{ab\left(a-b\right)}{\left(a-b\right)\left(a+b\right)}\)

\(=-1\) (đpcm )