Question

Из соотношения
((a+2b)/(a-b))^2 - 2*((a+2b)/(a-b))=3
выразите a через b

Answer 1

$\displaystyle \bigg(\frac{a+2b}{a-b}\bigg)^2-2\bigg(\frac{a+2b}{a-b}\bigg)=3\\\\\\\ \bigg(\frac{a+2b}{a-b}\bigg)^2-2\bigg(\frac{a+2b}{a-b}\bigg)+1=4\\\\\\\bigg(\frac{a+2b}{a-b}-1\bigg)^2=4\\\\\\\frac{a+2b}{a-b}-1=2\\\\\\a+2b-3(a-b)=0\\\\a+2b-3a+3b=0\\\\-2a+5b=0\\\\2a=5b\\\\\boxed{a=\frac{5}2b=2.5b}$