How do you simplify [\frac { x } { x - 2} - \frac { 2x } { x - 1} ][xx22xx1]?

1 Answer
Jun 30, 2017

It simplifies down to this: (-x^2 + 3x )/((x-2)(x-1))x2+3x(x2)(x1)

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)(x2)(x1), 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))x(x1)(x2)(x1)2x(x2)(x1)(x2)

Now multiply the numerators out to simplify each fraction:

(x^2 - x)/((x-2)(x-1)) - (2x^2-4x)/((x-2)(x-1))x2x(x2)(x1)2x24x(x2)(x1)

Make it all one fraction:

((x^2 - x) - (2x^2 - 4x))/((x-2)(x-1))(x2x)(2x24x)(x2)(x1)

Combine like terms:

(-x^2 +3x)/((x-2)(x-1))x2+3x(x2)(x1)

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