Question

Find 'b' in terms of 'a', if $x=\frac{2b-3}{b+2}$ and $a=\frac{2x-3}{x+2}$.

Answer 1

Given, $a=\frac{2x-3}{x+2}$
But $x=\frac{2b-3}{b+2}$
$=>a=\frac{2\left(\frac{2b-3}{b+2}\right)-3}{\frac{2b-3}{b+2}+2}$
$=>a=\frac{4b-6-3b-6}{2b-3+2b+4}$
$=>a=\frac{b-12}{4b+1}$
$=>4ab+a=b-12$
$=>b(4a-1)=-12-a$
$=>b(1-4a)=12+a$
$=>b=\frac{a+12}{1-4a}$