Question

Solve the following quadratic equations by factorization method:
$\frac{x}{x+1}+\frac{x+1}{x}=\frac{34}{15}$

• A. $\{-\frac{5}{2},\frac{3}{2}\}$
• B. $\{\frac{5}{2},\frac{3}{2}\}$
• C. $\{-\frac{5}{2},\frac{-3}{2}\}$
• D. None of these

Answer 1

The correct option is A $\{-\frac{5}{2},\frac{3}{2}\}$

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

$\Rightarrow$ $15x^2+15(x+1{)}^2=34x(x+1)$ [ multiplying both sides by $15x(x+1)$ ]

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

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

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

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

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

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

$\Rightarrow$ $2x+5=0$ and $2x-3=0$

$\therefore$ $x=-\frac{5}{2}$ and $x=\frac{3}{2}$