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

1 Answer
Jun 30, 2017

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!!!