Question

Given `f(x)=x/(x-1)`, how do you find the values of x for which `f(x)=2/3`?

Answer 1

`x = -2`

Explanation:

First, we must write this problem as"

`x/(x - 1) = 2/3`

To solve this we should first multiply this equation by a common denominator to eliminate the fractions and to keep the equation balanced. In this case we can multiply by `3(x - 1)`:

`((3(x - 1))x)/(x - 1) = ((3(x - 1))*2)/3`

`((3cancel((x - 1)))x)/(cancel(x - 1)) = ((cancel(3)(x - 1))*2)/cancel(3)`

`3x = (x - 1)2`

Next, we can expand the term in parenthesis:

`3x = 2x - 2`

Now we can isolate the `x` term on one side of the equation and the constant on the other side of the equation while keeping the equation balanced:

`3x - 2x = 2x -2x - 2`

`3x - 2x = 0 - 2`

Now we can consolidate likes terms to solve for `x`:

`(3 - 2)x = -2`

`1x = -2`

`x = -2`