Question

If $\frac{a-x}{b-x}=\frac{a^2}{b^2},$ then the value of x is

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

Answer 1

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

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

$\Rightarrow a{b}^2-b^{2}x=a^{2}b-a^{2}x$

$\Rightarrow a^{2}x-b^{2}x=a^{2}b-a{b}^2$

$\Rightarrow x(a^2-b^2)=ab(a-b)$

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

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