Question

Упростите выражение. ​

Answer 1

$1) \ \dfrac{1}{a+b}-\dfrac{a}{b^{2} +ab}=\dfrac{1}{a+b}-\dfrac{a}{b(b+a)}=\dfrac{b-a}{b(a+b)}\\\\\\2) \ \dfrac{b^{2} }{a^{3}-ab^{2}}- \dfrac{b}{a^{2}-ab }=\dfrac{b^{2} }{a(a^{2}-b^{2})}- \dfrac{b}{a(a-b) } =\\\\=\dfrac{b^{2} }{a(a-b)(a+b)}- \dfrac{b}{a(a-b) } =\dfrac{b^{2}-b(a+b) }{a(a-b)(a+b)} =\dfrac{b^{2}-ab-b^{2}}{a(a-b)(a+b)} =\\\\=\dfrac{ab}{a(b-a)(a+b)}=\dfrac{b}{(b-a)(a+b)}\\\\\\3) \ \dfrac{b-a}{b(a+b)}\cdot \dfrac{b}{(b-a)(a+b)}=\dfrac{1}{(a+b)^{2} }$