Question

Помогите пожалуйста упростить выражения, плизз

Answer 1

$1)\frac{x^{2}-y^{2}}{6xy}:\frac{x+y}{12x^{2}y}=\frac{(x-y)(x+y)}{6xy}*\frac{12x^{2}y}{x+y}=\boxed{2x(x-y)}\\\\\\2)\frac{a^{2}-25 }{a^{2}-3a}:\frac{a+5}{a^{2}-9 }=\frac{(a-5)(a+5)}{a(a-3)}*\frac{(a-3)(a+3)}{a+5}=\boxed{\frac{(a-5)(a+3)}{a}}\\\\\\3)\frac{2a^{6}b^{2}}{3c^{2} }*\frac{9b^{3}c^{3}}{8a^{4}}:\frac{3a^{2}b^{5}}{4c^{2}}=\frac{2a^{6}b^{2}}{3c^{2} }*\frac{9b^{3}c^{3}}{8a^{4}}*\frac{4c^{2}}{3a^{2}b^{5}}=\frac{a^{6}b^{5}c^{5}}{a^{6}b^{5}c^{2}}=\boxed{c^{3}}$

$4)\frac{8ab-8b^{2} }{a^{2}+ab }:\frac{4b^{3} }{a^{3}-ab^{2}}=\frac{8b(a-b)}{a(a+b)} *\frac{a(a-b)(a+b)}{4b^{3} }=\boxed{\frac{2(a-b)^{2} }{b^{2} }}\\\\\\5)\frac{a^{2}+b^{2}}{x^{3}+x^{2}y}:\frac{a^{4}-b^{4}}{x^{2}-y^{2}}=\frac{a^{2}+b^{2} }{x^{2}(x+y) }*\frac{(x+y)(x-y)}{(a^{2}+b^{2})(a^{2}-b^{2})}=\boxed{\frac{x-y}{x^{2}(a^{2}-b^{2})}}$