Question

Solve for $x$, if $\frac{x}{x+1}+\frac{x+1}{x}=\frac{34}{15}$

Answer 1

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

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

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

$\Rightarrow 15x^2+15x^2+15+30x=34x^2+34x$

$\Rightarrow 34x^2+34x-30x^2-30x-15=0$

$\Rightarrow 4x^2+4x-15=0$

$\Rightarrow 4x^2+10x-6x-15=0$

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

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