Question

Solve the following equations:

$\frac{(x-a)(x-b)}{x-a-b}=\frac{(x-c)(x-d)}{x-c-d}$

Answer 1

Subtracting x from both the members of the given equation, we get

$\frac{(x-a)(x-b)}{x-a-b}-x=\frac{(x-c)(x-d)}{x-c-d}-x$

or $\frac{ab}{x-a-b}=\frac{cd}{x-c-d}$

or $x(ab-cd)=ab(c+d)-cd(a+b)$

$\therefore$ $x=\frac{ab(c+d)-cd(a+b)}{ab-cd}$