Question

Simplify.\[\Large\tt\frac{8}{5b+2}+\frac{10}{3b-4}\]

Answer 1

I already know that the denominator would be (5b + 2)(3b - 4). I just need help with the numerator.

Answer 2

wait i'll solve

Answer 3

2(37b−6)(3b−4)(5b+2)

Answer 4

Did you mean: \[\frac{2(37-6)}{(3b-4)(5b+2)}\]

Answer 5

yea

Answer 6

How did you get that answer? :)

Answer 7

I think I know, but I am not sure. Let me finish what I was doing offline and see if I get the same answer.

Answer 8

ok

Answer 9

Can you show me the steps you took to get your answer? @MGLMystiicz

Answer 10

@rational Can you help me? :)

Answer 11

\[\tt\frac{8}{5b+2}+\frac{10}{3b-4}\]

You have two fractions with different denominators, so you cannot combine them directly.

Answer 12

Get common denominator first

Answer 13

The common denominator is (5b + 2)(3b - 4).

Answer 14

multiply top and bottom of first fraction by 3b-4
multiply top and bottom of second fraction by 5b+2

\[\tt\frac{8(3b-4)}{(5b+2)(3b-4)}+\frac{10(5b+2)}{(3b-4)(5b+2)}\]

Answer 15

Now that the bottoms of both fractions are same, you may add the numerators and put the common denominator below them :

\[\tt\frac{8(3b-4)+10(5b+2)}{(5b+2)(3b-4)}\]

Answer 16

simplify the numerator

Answer 17

Mhmm. And do we multiply the numerators and then add them? :)

Answer 18

yes

Answer 19

\[\tt\frac{24b-4}{(5b+2)(3b-4)}+\frac{50b+2}{(3b-4)(5b+2)}\] @rational

Answer 20

yes, add the numerators and put the common denominator below them

Answer 21

\[\tt\frac{24b-4+50b+2}{(3b-4)(5b+2)}\]

Answer 22

@rational ^

Answer 23

numerator can be simplified further

Answer 24

combine like terms in numerator

Answer 25

\[\tt\frac{74b-2}{(3b-4)(5b+2)}\]

Answer 26

@rational ^

Answer 27

Hey, Mr. @rational, you still there? ._.

Answer 28

looks good, also you may factor out "2" from numerator

Answer 29

How? :)

Answer 30

\[\tt\frac{74b-2}{(3b-4)(5b+2)}\]

\[\tt\frac{2(37b-1)}{(3b-4)(5b+2)}\]