Question

factrolization
a÷x-a +b÷x-b =2c÷x-c​

Answer 1

Solution

We have,

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

Given Expression can also be written as:

$\implies \ \: \sf{ \frac{a}{x - a} + \frac{b}{x - b} = \frac{c + c}{x - c} } \\ \\ \implies \: \sf{ \frac{a}{x - a} + \frac{b}{x - b} = \frac{c}{x - c} + \frac{c}{x - c}} \\ \\ \implies \: \sf{ \frac{a}{x - a} - \frac{c}{x - c} = \frac{c}{x - c} - \frac{b}{x - b}} \\ \\ \implies \: \sf{ \frac{a(x - c) - c(x - a)}{(x - a) \cancel{(x - c)}} = \frac{c(x - b) - b(x - c)}{(x - b) \cancel{(x - c)}} } \\ \\ \implies \: \sf{ \frac{ax - \cancel{ac} - cx + \cancel{ac}}{x - a} = \frac{cx - \cancel{bc} - bx + \cancel{bc}}{x - b}}$