Question

упростите выражение (1/a²+2ab-1/a²+2ab):4b²/4b²-a²
дам 20 баллов​

Answer 1

$\Big(\dfrac{1}{a^{2}+2ab }-\dfrac{1}{a^{2}-2ab} \Big) :\dfrac{4b^{2} }{4b^{2} -a^{2} } =\Big(\dfrac{1}{a(a+2b)}-\dfrac{1}{a(a-2b)}\Big)\cdot\dfrac{(2b-a)(2b+a)}{4b^{2} }=\\\\=\dfrac{a-2b-a-2b}{a(a+2b)(a-2b)}\cdot\dfrac{(2b-a)(2b+a)}{4b^{2} }=\dfrac{-4b}{a(a-2b)}\cdot\dfrac{2b-a}{4b^{2} } =\\\\=\dfrac{4b\cdot(a-2b)}{a(a-2b)\cdot4b^{2} }=\boxed{\dfrac{1}{ab}}$