Can someone show me step by step how to get the answers, the book is really confusing?

Question

Perform the indicated operation
4/x+2 - 7/x^2-4

and
1/x-7 +8

Answer 1

1.

4/(x + 2) - 7/(x^2 - 4)

First you have to get a common denominator.
We notice that the second denominator (x^2 - 4) is a difference of squares, so we can factor it into (x - 2)(x + 2). Now we can see that the first denominator is part of the second denominator.

So to get a common denominator we just need to multiply the first fraction by the difference, which is (x - 2). So the first fraction becomes:

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

Now we can subtract them easily.

4(x - 2)/(x + 2)(x - 2) - 7/(x + 2)(x - 2)
= (4x - 8 - 7)/(x + 2)(x - 2)
= (4x - 15)/(x + 2)(x - 2)

2.

1/(x - 7) + 8

We do the same thing with this fraction. First get a common denominator.

The denominator of a whole number is just 1, so we need to multiply the 8 by (x - 7). So now we have:

1/(x - 7) + 8(x - 7)/(x - 7)
= (1 + 8x - 56)/(x - 7)
= (8x - 55)/(x - 7)

Answer 2

1st question: combine the like terms. 4/x - 7/x = -3/x.
2 - 4 = -2, +2 - 2 = 0
so u are now left with -3/x ^ 0 which equals....im not sure but im sure its easy.

1/x-7 +8 is easy. -7 +8 =1
1/x-1 is your answer