Question

$\text{Find the value of x in the equation}\frac{x}{x-a}+\frac{x}{x-b}=2.$

• A. $\frac{a}{b}$
• B. $ab$
• C. $\frac{2ab}{a+b}$
• D. $2ab$

Answer 1

The correct option is C $\frac{2ab}{a+b}$

$\text{Given:}\frac{x}{x-a}+\frac{x}{x-b}=2$

$\frac{x}{x-a}+\frac{x}{x-b}=2$

By taking the LCM,

$\Rightarrow \frac{x(x-b)+x(x-a)}{(x-a)(x-b)}=2$

$\Rightarrow x^2-xb+x^2-xa=2\left[\right(x-b\left)\right(x-a\left)\right]$

$\Rightarrow 2x^2-xb-xa=2[x^2-xb-ax+ab]$

$\Rightarrow 2x^2-xb-xa=2x^2-2xb-2ax+2ab$

$\Rightarrow 2x^2-2x^2-xb+2xb-xa+2xa=2ab$

$\Rightarrow xb+ax=2ab$

$\Rightarrow x(a+b)=2ab$

$\Rightarrow x=\frac{2ab}{a+b}$