Question

Solve for x: a/(ax-1) + b/(bx-1) = a+b ; x is not equal to 1/a, 1/b

Answer 1

hope this may help you

Answer 2

Answer:

The value of x is 2/( a+b-ab)

Step-by-step explanation:

Given Data: a/(ax-1) + b/(bx-1) = a+b ; To find the value of x:  

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

Step 1:

(abx - a +abx-b)/(ax-1)(bx-1) = a+b

$2 a b x-a-b=(a+b)\left(a b x^{2}-a x-b x+1\right)$

Step 2:

$2 \mathrm{abx}-\mathrm{a}-\mathrm{b}=\mathrm{a}^{2} \mathrm{bx}^{2}-\mathrm{a}^{2} \mathrm{x}-\mathrm{abx}+\mathrm{a}+\mathrm{ab}^{2} \mathrm{x}^{2}-\mathrm{abx}-\mathrm{b}^{2} \mathrm{x}+\mathrm{b}$

Step 3:

$\left.\begin{array}{l}{x\left(2 a b-a^{2} b+a^{2}-a b^{2}+b^{2}\right)=2 a+2 b} \\ {x\left[(a+b)^{2}-a^{2} b-a b^{2}\right]=2 a+2}\end{array} \quad \text { (therefore, }(a+b)^{2}=a^{2}+b^{2}+2 a b\right)$

Step 4:

x = 2(a+b)/(a+b)(a+b-ab)    (cancelling a+b)

x = 2/( a+b-ab)