Question

solve for x correctly​

Answer 1

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Answer 2

QUESTION

Solve for x : $\frac{a}{ax - 1} + \frac{b}{bx - 1} = a + b$

Where , $x \neq \: \frac{1}{a} \: \: \frac{1}{b}$

SOLUTION

$\: \: \: \: \: \: \frac{a}{ax - 1} + \frac{b}{bx - 1} = a + b \\ \\ \\ = > \frac{a}{ax - 1} - b = a - \frac{b}{bx - 1} \\ \\ \\ = > \frac{a - abx + b}{ax - 1} = \frac{abx - a - b}{bx - 1} \\ \\ \\ = > (a - abx + b)(bx - 1) = (abx - a - b)(ax - 1) \\ \\ \\ = > \frac{a - abx + b}{abx - a-b } = \frac{ax - 1}{bx - 1} \\ \\ \\ = > \frac{a + b - abx}{ - (a + b - abx) } = \frac{ax - 1}{bx - 1} \\ \\ \\ = > - 1 = \frac{ax - 1}{bx - 1} \\ \\ \\ = > ax - 1 = ( - 1) \times (bx - 1) \\ \\ \\ = > ax - 1 = - bx + 1 \\ \\ \\ = > ax + bx = 1 + 1 \\ \\ \\ = > x(a + b) = 2 \\ \\ \\ = > x = \frac{2}{a + b}$

ANSWER $\underline { \: \: \: \boxed{ \boxed{ \: \: \: x = \frac{2}{a + b} }} \: \: \: \: }$