(a-x)/(b-x)=c/(x-b)
How do i go about solving this?
To solve the given equation: (a - x) / (b - x) = c / (x - b), we can start by cross-multiplying.
First, multiply both sides of the equation by (b - x) and (x - b) in order to eliminate the denominators:
(b - x) * (x - b) * (a - x) = (b - x) * (x - b) * (c / (x - b))
Expanding both sides of the equation gives:
(a - x) * (x - b) * (b - x) = c * (x - b)
Now, simplify the equation further:
(a - x) * (b - x) * (x - b) = c * (x - b)
Expanding the equation gives:
(a - x) * (b - x + x - b) = c * (x - b)
Simplifying the equation gives:
(a - x) * (-b) = c * (x - b)
Distribute the negative sign:
(-a + x) * (-b) = c * (x - b)
Simplifying further gives:
ab - xb = cx - cb
Rearrange the equation by adding xb and subtracting cx from both sides:
ab - cb = cx - xb + xb - cx
Simplify this equation:
ab - cb = 0
Finally, we can solve for x:
ab - cb = 0
ab = cb
Dividing both sides by b gives:
a = c
Therefore, the solution to the given equation is x = a, under the condition that a is not equal to b.