Question

What is the sum 1/g+2 +3/g+1

a. 3/g+3
b. g+3/(g+1)(g+2)
c. 4g+7/(g+1)(g+2)
d. 2g+3/(g+1)(g+2)

Answer 1

what common denominator can you use ?

Answer 2

g+3?

Answer 3

no, the common denominator is not g+3

I would multiply the two denominators to get a common denominator

Answer 4

notice most of your answer choices do that

Answer 5

ok so its (g+1)(g+2)

Answer 6

yes. next, what do you multiply the first fraction by so you get that denominator ?
remember you multiply top and bottom by the same thing

Answer 7

(1)(g+1)?

Answer 8

yes, and you do that in the bottom also so that you get
\[ \frac{g+1}{(g+1)(g+2) }\]

Answer 9

now what about the second fraction?

Answer 10

(3)(g+2)=3g+2?

Answer 11

close. you have 3 "packages" of (g+2)
which means you have 3 of everything inside the package

in other words, redo this part :3(g+2) becuase it's not 3g+2.

Answer 12

ok

Answer 13

do you get the idea? 3(g+2) means the same as (g+2)+(g+2) + (g+2)
how many g's is that ? how many 2's ?

Answer 14

3 gs and 3 2s

Answer 15

and you can write that as
3g+3*2
or 3g+2+2+2
but most people would write it
3g+6

Answer 16

ok

Answer 17

now both fractions have the same denominator.
you can add their "tops"

Answer 18

so it would be 4g+7/(g+1)(g+2)

Answer 19

yes