Question

solve for x :(a/x-a) + (b/x-b) =2 ; x not equal to a,b

Answer 1

I hope it will help you. :-

Answer 2

Answer:

x= [3(a+b)±√9a²+9b²-14ab]/4

Explanation:

We have

$\frac{a}{(x-a)}+\frac{b}{(x-b}=2$

LCM of (x-a)and (x-b) = (x-a)(x-b)

Now,

$\frac{a(x-b)+b(x-a)}{(x-a)(x-b)}=2$

$\implies \frac{ax-ab+bx-ab}{x^{2}-ax-bx+ab}=2$

$\implies ax+bx-2ab=2(x^{2}-ax-bx+ab)$

$\implies 0=2x^{2}-2ax-2bx+2ab-ax-bx+2ab$

$\implies 2x^{2}-3(a+b)x+4ab=0$

Compare this with Ax²+Bx+C=0

we get,

A=2 , B = -3(a+b), C = 4ab

Discreminant (D) = B²-4AC

= [-3(a+b)]²-4×2×4ab

= 9(a+b)²-32ab

= 9(a²+b²+2ab)-32ab

= 9a²+9b²+18ab-32ab

= 9a²+9b²-14ab

Now ,

x = [-B±√D]/(2A)

= {-[-3(a+b)]±√9a²+9b²-14ab}/4

x= [3(a+b)±√9a²+9b²-14ab]/4

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