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

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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.

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