Addition and Subtracting Variables 2?

Question

3x/x-4 + 4/x+4

How to solve?

Answer 1

Without an = sign, you can't SOLVE...but you could combine.

I'm assuming you mean:

3x/(x - 4) + 4/(x + 4)

So, like when you add fractions, you need a common denominator. That common denominator is (x - 4)(x + 4).

So multiply the first term by (x + 4)/(x + 4):

3x/(x - 4) (x + 4)/(x - 4) = 3x(x + 4)/[(x - 4)(x + 4)] = (3x² + 12x)/(x² - 16)

And the second term by (x - 4)/(x - 4):

4/(x + 4) (x - 4)/(x - 4) = 4(x - 4)/[(x + 4)(x - 4)] = (4x - 16)/(x² - 16)

Now you have a common denominatory so you can combine:

(3x² + 12x + 4x - 16)/(x² - 16)
= (3x² + 16x - 16)/(x² - 16)

The numerator doesn't factor without using the quadratic formula, so I'd leave it that way.

Answer 2

3x/x-4 + 4/x+4

= [3x(x+4) + 4(x-4)]/(x-4)(x+4)
= (3x^2 + 12x + 4x - 16)/(x^2 - 16)
= (3x^2 + 16x - 16)/(x^2 - 16)