Makr x subject of fomuka the x/x+a-a/x+b=1

3 answers

To make "x" the subject of the equation:

f(x) = the original equation = (x/x+a) - (a/x+b) = 1

1. Multiply both sides by (x+a)(x+b):
(x/x+a) - (a/x+b) = 1
(x+b) - a(x+a)(x/x+a) = (x+a)(x+b)
(x+b) - ax(x+a) = (x+a)(x+b)

2. Expand the equation:
(x+b) - ax² - a²x = x² + ax + xb + ab
x + b - ax² - a²x = x² + ax + xb + ab

3. Rearrange the terms:
x² + ax + ab + xb - ax² - a²x - x - b = 0

4. Group similar terms:
x² - ax² + xb - a²x + ax + x - b - ab = 0

5. Combine like terms:
(1 - a)x² + (x - a² - ab + 1)x - b = 0

Now, "x" is the subject of the equation: x = (- (x - a² - ab + 1) ± √((x - a² - ab + 1)² - 4(1 - a)(-b))) / (2(1 - a))
what a load of rubbish! And at the end, you didn't even solve for x, since it appears on both sides of the equation!

x/(x+a) - a/(x+b) = 1
x(x+b) - a(x+a) = (x+a)(x+b)
x^2 + bx - ax - a^2 = x^2 + ax + bx + ab
bx - ax - bx - ax = ab + a^2
-2ax = a(a+b)
x = -(a+b)/2
Apologies for the mistake in the previous response. You are correct, and the correct solution for making "x" the subject of the equation is:

x/(x+a) - a/(x+b) = 1

Multiplying both sides by (x+a)(x+b):

x(x+b) - a(x+a) = (x+a)(x+b)

Expanding:

x^2 + bx - ax - a^2 = x^2 + ax + bx + ab

Combining like terms:

-2ax = a^2 + ab

Dividing both sides by -2a:

x = -(a^2 + ab)/(2a)

Simplifying:

x = -(a+b)/2