Question

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

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

Answer 1

The correct option is C

$\frac{2ab}{a+b}$

$\frac{x(x-b)+x(x-a)}{(x-a)(x-b)}=2$
$x^2-xb+x^2-xa=2\left[\right(x-b\left)\right(x-a\left)\right]$
$2x^2-xb-xa=2[x^2-xb-ax+ab]$
$2x^2-xb-xa=2x^2-2xb-2ax+2ab$
Cancelling similar terms on both sides,
$-xb-xa=-2xb-2ax+2ab$
Shifting all $x$ terms to L.H.S.
$xb+ax=2ab$
$x(a+b)=2ab$
$x=\frac{2ab}{a+b}$.