Question

Solve for x (in terms of a and b)
a/x-b+b/x-a=2,x not equal to a,b

Answer 1

=>  Answer:

x = (a+b)/2 or x = a+b

=>  Step-by-step explanation:

• ∴ a / (x-b) + b / (x-a) = 2

• ∴ a(x-a) + b(x-b) = 2(x-a) ( x-b)

• ∴ ax+bx-a²-b² = 2x²-2bx-2ax+2ab

• ∴ -a²-b² = 2x²-3(a+b)x +2ab

• ∴ 2x²-3(a+b)x+(a+b)²=0

• ∴ 2x²-2(a+b)x-(a+b)x+(a+b)²= 0

• ∴ 2x [x-(a+b)]-(a+b) [x-(a+b)]= 0

• ∴ x = a+b or x= (a+b)/2

=>x = a+b

=>x = (a+b)/2