Question

Solve:a/ax-1 + b/bx-1=a+b

Answer 1

$\frac{a}{ax-1}+\frac{b}{bx-1} = a+b \\ \\ \\ \implies \frac{a}{ax-1}-b = a - \frac{b}{bx-1} \\ \\ \\ \implies \frac{a-b(ax-1)}{ax-1} = \frac{a(bx-1)-b}{bx-1} \\ \\ \\ \implies \frac{a-abx+b}{ax-1}=\frac{abx-a-b}{bx-1} \\ \\ \\ \implies \frac{a+b-abx}{ax-1} = \frac{-(a+b-abx)}{bx-1} \\ \\ \\ \implies a+b-abx=0 \text{ is a possible solution} \\ \\ \\ \implies \frac{\cancel{a+b-abx}}{ax-1} = \frac{-\cancel{a+b-abx}}{bx-1} \\ \\ \\ \implies \frac{1}{ax-1} = -\frac{1}{bx-1} \\ \\ \\ \implies bx-1 = -(ax-1)$


$\implies bx-1 = -ax+1 \\ \\ \\ \implies bx+ax=2 \\ \\ \\ \implies (a+b)x=2 \\ \\ \\ \implies \boxed{\bold{x=\frac{2}{a+b}}}$

Also, as mentioned above, a+b-abx=0 is also a solution.

$a+b-abx=0 \\ \\ \\ \implies abx=a+b \\ \\ \\ \implies \boxed{\bold{x=\frac{a+b}{ab}}}$



Thus, The Solutions are:



$\bold{x = \frac{a+b}{ab}} \quad and \quad \bold{x = \frac{2}{a+b}}$

Answer 2

Given Expression :
$\frac{a}{ax - 1} - \frac{b}{bx - 1} = a + b$
To Find :

The required solutions.


Solution :

Refer to the above Attachments !!

The required solutions :


1) => x =
$\frac{2}{a + b}$

2) => x =
$\frac{a + b}{ab}$
#Be Brainly !!