Question

Solve :

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

Answer 1

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

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

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

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

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

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

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

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

$x=\frac{3}{2},\frac{-5}{2}$