Question

Which of the following is the simplified form of x minus 7 over 2 x minus 12 plus the fraction 6 over x squared minus 36 ?

Answer 1

look at the denominators tell me if you can find another form of representing them

Answer 2

for example 2x-12 = 2(x-6)
what about x^2 - 36 ?

Answer 3

(x - 6)(x + 6)

Answer 4

good
so now find a common denominator for the expression

Answer 5

I'm not sure

Answer 6

2(x-6)(x+6) cause it will contain the terms from both

Answer 7

Okay.

Answer 8

what the expression would look like after the common denominator ?

Answer 9

x + 5/2(x - 6)

Answer 10

in the first term we have 2(x-6) in the denominator so we have to multiply it by x+6

Answer 11

so for the first term we will get
(x-7)(x+6) / 2(x-6)(x+6)

Answer 12

for the second term we have to multiply it only by 2 since we have (x-6)(x+6)

Answer 13

so the second term will become 12/(x-6)(x+6)

Answer 14

the whole expression : [(x-7)(x+6) + 12] / 2(x+6)(x-6)

Answer 15

now you can arrange the terms in the nominator

Answer 16

can you do it ?

Answer 17

anyway since i have to go i solved it:
(x+5) / 2(x+6)