Question

The values of $x$ satisfying the equation ${\left(\frac{x}{x+1}\right)}^2-5\left(\frac{x}{x+1}\right)+6=0$ are

• A. $2,\frac{3}{2}$
• B. $2,-\frac{3}{2}$
• C. $-2,\frac{3}{2}$
• D. $-2,-\frac{3}{2}$

Answer 1

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

Given equation is:

${\left(\frac{x}{x+1}\right)}^2-5\left(\frac{x}{x+1}\right)+6=0$

Let, $\frac{x}{x+1}=y$
$\Rightarrow y^2-5y+6=0$
$\Rightarrow (y-2)(y-3)=0$
$\Rightarrow y=2,y=3$
$\Rightarrow \frac{x}{x+1}=2;\frac{x}{x+1}=3$
$\Rightarrow x=2x+2;x=3x+3$

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