Can someone please help me?? I don't understand...?

Question

1. Add. Express in Simplest form:
(x^2) over (x+4) + (2x-8) over (x+4)

2. Multiply:
(4x-24) over (x^2-2x) * (8x) over (6-x)

Answer 1

1. Add. Express in Simplest form:
(x^2) over (x+4) + (2x-8) over (x+4)

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

The key part is factoring, because then you get a factor of x+4 in both the numerator and denominator. The x+4 cancels from the numerator and denominator, leaving just x-2 for the answer.

2. (4x-24) over (x^2-2x) * (8x) over (6-x)

4(x-6)/x(x-2) * 8x/(6-x)

You could multiply it all out, and then cancel like terms from the numerator and denominator... but I'd cancel x from the numerator and denominator, and also x-6 vs 6-x (leaving only -1):

4(x-6)/x(x-2) * 8x/(6-x) =
-4/(x-2) * 8 =
-32 / (x - 2)

Answer 2

This is a simplification problem. They are asking you to calculate the fractions and reduce them to as few terms as possible.... Here's the first one:

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

You can work the second one similiarly. Try to get it down to just a couple terms.

Answer 3

X^2/(X+4) + ( 2X-8)/(X+4) =

(X^2 + 2X - 8)/(X+4) =

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

2. 4(X-6)/(X(X-2)) * 8 X/(6-X) = -32/(X-2)

Answer 4

the first one u just add them together since the denominator is the same.
it will be (x^2)) + 2x+8) all over (x+4)

the bottom one you just multiply so it would be (32x^2-192x) all over 6x^2-12x-(x^3)+2x^2 so that is 8x^2-12x-(x^3)

then simplify