Question

Solve the given quadratic equation by factorization method
$\frac{x}{x+1}+\frac{x+1}{x}=\frac{34}{15},x\ne 0,x\ne -1$

Answer 1

Given : $\frac{x}{x+1}+\frac{x+1}{x}=\frac{34}{15},x\ne 0,x\ne -1$

$\Rightarrow \frac{x^2+{(x+1)}^2}{x(x+1)}=\frac{34}{15}\Rightarrow \frac{x^2+x^2+2x+1}{x^2+x}=\frac{34}{15}$

$\Rightarrow 34x^2+34x=15x^2+15x^2+30x+15\Rightarrow 4x^2+4x-15=0\Rightarrow 2x(2x+5)-3(2x+5)=0$

$\Rightarrow (2x-3)(2x+5)=0$

$\Rightarrow (2x-3)(2x+5)=0\Rightarrow 2x-3=0or2x+5=0$

$\Rightarrow x=\frac{3}{2}orx=-\frac{5}{2}$