How do you simplify #(2x) /( x + 4) - (x )/ (x-4)#?

Question

1470 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-13T12:33:39

#(x^2-12x)/((x+4)(x-4))#

We have:

#(2x)/(x+4)-x/(x-4)#

Take the #"LCM"# of both denominators, which is #(x+4)(x-4)#, and so we got:

#(2x(x-4))/((x+4)(x-4))-(x(x+4))/((x+4)(x-4))#

We know that: #a/c-b/c=(a-b)/c#

So, we got:

#=(2x(x-4)-x(x+4))/((x+4)(x-4))#

Expand the numerator to get:

#=(2x^2-8x-x^2-4x)/((x+4)(x-4))#

#=(x^2-12x)/((x+4)(x-4))#

This cannot be simplified further, and thus is the answer itself.