Question

What solves the equation? (Needs to be simplified)

Answer 1

`\bf \cfrac{4v+1}{6v^2-19v+10}/ \boxed{x}=\cfrac{4v-1}{3v-2}\implies \cfrac{~~(4v+1)/(6v^2-19v+10)~~}{x}=\cfrac{4v-1}{3v-2} \\\\\\ \stackrel{\textit{cross-multipying}}{\cfrac{~~(4v+1)/(6v^2-19v+10)~~}{(4v-1)/(3v-2)}=x}\implies \cfrac{4v+1}{6v^2-19v+10}\cdot \cfrac{3v-2}{4v-1}=x \\\\\\ \cfrac{4v+1}{(\underline{3v-2})(2v-5)}\cdot \cfrac{\underline{3v-2}}{4v-1}=x\implies \cfrac{4v+1}{(2v-5)(4v-1)}=x \\\\\\ \cfrac{4v+1}{8v^2-2v-20v+5}=x\implies \cfrac{4v+1}{8v^2-22v+5}=x`