Question

Solve each of the following quadratic equations:
$\frac{x}{x+1}+\frac{x+1}{x}=2\frac{4}{15},x\ne 0,-1$

Answer 1

$\frac{x}{x+1}+\frac{x+1}{x}=2\frac{4}{15}\frac{x}{x+1}+\frac{x+1}{x}=\frac{34}{15}\frac{x^2+(x+1{)}^2}{x(x+1)}=\frac{34}{15}\frac{x^2+x^2+2x+1}{x^2+x}=\frac{34}{15}$

$\Rightarrow 15(2x^2+2x+1)=34(x^2+x)\Rightarrow 30x^2+30x+15=34x^2+34x\Rightarrow 34x^2–30x^2+34x–30x–15=0\Rightarrow 4x^2+4x–15=0\Rightarrow 4x^2+10x–6x–15=0\Rightarrow 2x(2x+5)–3(2x+5)=0\Rightarrow (2x–3)(2x+5)=0$

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