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

Answer 1

Eva Adamson

#(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.

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Answer 2

Jameson Allen

To simplify the expression (2x) / (x + 4) - (x) / (x-4), we need to find a common denominator for the two fractions. The common denominator is (x + 4)(x - 4).

Multiplying the first fraction by (x - 4) / (x - 4) and the second fraction by (x + 4) / (x + 4), we get:

[(2x)(x - 4)] / [(x + 4)(x - 4)] - [(x)(x + 4)] / [(x + 4)(x - 4)]

Expanding and simplifying the numerators, we have:

(2x^2 - 8x - x^2 - 4x) / [(x + 4)(x - 4)]

Combining like terms in the numerator, we get:

(x^2 - 12x) / [(x + 4)(x - 4)]

Therefore, the simplified expression is (x^2 - 12x) / [(x + 4)(x - 4)].

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.