Question

Solve the quadratic equation by factorization method.

$\frac{x}{x+1}+\frac{x+1}{x}=\frac{34}{15}$

Answer 1

Given quadratic equation is

$\frac{x}{x+1}+\frac{x+1}{x}=\frac{34}{15}$

$⟹15[x^2+(x+1{)}^2]=34[x(x+1)]$

$⟹15[2x^2+2x+1]=34[x^2+x]$

$⟹30x^2+30x+15=34x^2+34x$

$⟹4x^2+4x-15=0$

$⟹4x^2+10x-6x-15=0$

$⟹2x(2x+5)-3(2x+5)=0$

$⟹(2x+5)(2x-3)=0$

$⟹2x+5=0,2x-3=0$

$⟹x=\frac{3}{2},\frac{-5}{2}$