Question

How do you simplify `[\frac { x } { x - 2} - \frac { 2x } { x - 1} ]`?

Answer 1

It simplifies down to this: `(-x^2 + 3x )/((x-2)(x-1))`

Explanation:

First things first, we have to find a common denominator by finding the least common multiple. In this case, the least common multiple of both the fractions is `(x-2)(x-1)`, and therefore will serve as our common denominator. Go ahead and multiply the fractions respectively to get to the common denominator.

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

Now multiply the numerators out to simplify each fraction:

`(x^2 - x)/((x-2)(x-1)) - (2x^2-4x)/((x-2)(x-1))`

Make it all one fraction:

`((x^2 - x) - (2x^2 - 4x))/((x-2)(x-1))`

Combine like terms:

`(-x^2 +3x)/((x-2)(x-1))`

And you're done! Hope this helps!!!