Question

please help
(x/x + 3) + (x + 2/x + 5)

Answer 1

First you need to create a common denominator. Do you know how?

Answer 2

would that be like x + 15

Answer 3

No It would be (x+3)(x+5)

Answer 4

oh ._. lol then what?

Answer 5

You would need to multiply that common denominator towards our numerators.

Answer 6

Like so, \[\frac{ x(x+5) }{ (x+3)(x+5) }\]

Answer 7

Yes like @Johnbc said whatever you multiply the denominator by you must also do to the numerator

Answer 8

Because the only term missing was (x+5) to get our common denominator we only had to multiply by that and to the other term you can already tell it is only missing (x+3) so multiply the other term by that and add them over your new common denominator.

Answer 9

so what would it look like when the two numerators are added

Answer 10

\[\frac{ x(x+5) + (x+2)(x+3) }{ (x+3)(x+5) }\]

Answer 11

You know have to perform the multiplication to get your new terms and then combine like terms.

Answer 12

\[2x^2 + 10x + 6 \ \]

Answer 13

Correct that is the numerator

Answer 14

and then you have to factor?

Answer 15

Well you also have a denominator.

Answer 16

\[\frac{ 2x^2+10x+6 }{ x^2+8x+15 }\]

Answer 17

ok cool, ^ is that simplified?

Answer 18

Nope.

Answer 19

You can cancel stuff out and simplify further now.

Answer 20

If you leave the denominator factored and perform the operation you said it is actually easier.

Answer 21

\[\frac{ 2(x^2+5x+3) }{ (x+3)(x+5) }\]

Answer 22

ok now I think that is totally factored

Answer 23

Yeah that would be close to a factored answer

Answer 24

thanks so much for holding my hand through this lol!

Answer 25

My pleasure

Answer 26

If you are asked to perform the division you can actually get a more simplified value.