Question

simplify. state restrictions. 7x/x+4 + 3x/x-6

Answer 1

well, the denominator cannot be 0

Answer 2

how would I simplify though

Answer 3

im going to assume that your question is

simplify
\[\frac{7x}{x+4}+\frac{3x}{x-6}\]

well in order to add fractions together, they need to have the same denominator

so you first need to determine what lcd or gcm or gcd or whatever its called

once you figure that out, you need to determine what you must multiply to each fraction seperately so they then have the same denominator,

Answer 4

yes I just needed help to determine the LCD. Wouldn't it be x^2-12 ?

Answer 5

how did you get that?

Answer 6

well the lcd for 4 and 6 is 12

Answer 7

or would it be 12x-12? :S im not sure

Answer 8

yes normally that is true, but in your case, you're not just dealing with 4 and 6

you're dealing with (x+4) and (x-6)

Answer 9

oh okay, so how would I determine the lcd

Answer 10

well you dont really need to determine lcd, you just want the 2 fractions to have common denominator

the simpliest way would jsut be to multiply the 2 denominators together

so the denonminator would be (x+4)*(x-6)

if you want to expand that, go for it, but you can just leave it as is


once you determine that the denominator will be (x+4)(x-6)

you need to multiply each fraction by something so they will be fractions with that denominator

Answer 11

okay thank you so much, I understand now

Answer 12

just to make sure, for the first fraction, you would have to multiply it by (x-6)/(x-6)

so what would you need to multiply to the 2nd fraction?