8 over x+4 + 3 over x-4?

Question

8 over x+4 + 3 over x-4 add

Answer 1

8/(x+4)+3/(x-4)
=(8*(x-4)+3*(x+4))/((x+4)*(x-4))
=(11x-20)/(x^2-16)

Answer 2

x=4

Answer 3

The first answer is correct. I am answering here to show you the work a little more clearly.

The first thing you need to do is find a common denominator. Since the denominators don't share any common factors, you can find their least common multiple just by multiplying them together. Thus the common denominator is (x+4)(x-4) = x^2 - 16.

To put the first fraction over x^2 - 16, you have to multiply the top and bottom both by (x - 4), so it becomes

8(x - 4).............8x - 32
---------------- = -----------
(x+4)(x-4)....... x^2 - 16

To put the second fraction over x^2 - 16, you have to multiply the top and bottom both by (x + 4), so it becomes

3(x + 4)..........3x + 12
-------------- = -----------
(x-4)(x+4).......x^2 - 16

Now you just add the numerators and keep the denominator the same.

8x -32 + 3x + 12 .......11x - 20
------------------------ = --------------
.....x^2 - 16................ x^2 - 16


(The dots are to get the spacing right... couldn't do it with spaces)

Answer 4

(8/(x + 4)) + (3/(x - 4))
multiply everything by (x + 4)(x - 4)
(8(x - 4) + 3(x - 4))/((x + 4)(x - 4))
(8x - 32 + 3x - 12)/((x + 4)(x - 4))
(11x - 44)/((x + 4)(x - 4))
(11(x - 4))/((x + 4)(x - 4))

ANS : 11/(x + 4)

Answer 5

11/x

Answer 6

11over 2x