Question

solve for x/a-x + b/x-b=-2

Answer 1

Step-by-step explanation:

\frac{a}{x-b} +\frac{b}{x-a}=2 \:\:\:(*(x-a)(x-b))\\a(x-a) + b(x-b) =2 (x-a)(x-b)\\ax - a^2 + bx - b^2 = 2 (x-a) (x-b) \\ax - a^2+ bx - b^2 = (2x-2a) (x-b) \\ax - a^2 + bx - b^2 = 2x^2 - 2bx - 2ax + 2ab \\-2x^2 + 3bx + 3ax - a^2 - b^2 - 2ab = 0 \\2x^2 - 3bx - 3ax + a^2 + b^2 +2ab = 0 \\2x^2 - 3 (a+b) x + (a+b)^2 = 0 \\2x^2 - 2(a+b)x - 1(a+b)x + (a+b)^2 = 0 \\2x [x - (a+b)] - (a+b) [x - (a+b)] = 0 \\(2x - a - b ) (x - a - b) = 0 \\2x - a - b = 0\:\:\:\:OR\:\:\:\:x - a - b = 0

Therefore,

x = a+b / 2\:\:\:OR\:\:\:x = a + b