Rational expressions

[green linden]

I know that i factor out the 6x+6 and thhe 4x-12 but i dont know what to do after

[light hearth]

Factor out? Alright first of all, how do you add fractions?

sorry fish-

[last forge]

no, i thought i pretty much gave away the answer.

[green linden]

first you need to have a like denominator

then you add the numerator

[light hearth]

Right, so in this case, how are you gonna get a like denominator?

[green linden]

well what my teacher does first is always factor what ever you can

[light hearth]

ignore the numerators for now

[green linden]

like my teacher would factor out the 6 in 6x+6

and then you would have 6(x+1)

[light hearth]

huh... well, tbh I'm not 100% sure I can explain why or how to use that method, but my method is simply to put both denominators in brackets next to each other and call it a day

like (6x + 6)(4x - 12)

that becomes your new denominator

after doing that, you multiply the respective numerator by the opposing denominator. So x will multiply by (4x - 12) and 5 will multiply by (6x + 6)

then u simply multiply that out, and then add the numerators

[green linden]

So then you just have one big expression like x+5/(6x+6)(4x-12)?

[light hearth]

It would become one big expression but it wouldn't be exactly like that

remember whatever you multiply your denominator by, you have to multiply your numerator as well

[green linden]

oh yeah lol i forgot

So then would it be

x(4x-12)+5(6x+6)/4x-12)(6x+6)

[light hearth]

bingo

[green linden]

I see and then you just expand?

[light hearth]

yep

[green linden]

so then you would get 4x^2+18x+30

then i would divide by two

[light hearth]

gimme a sec

[light hearth]

this is the right numerator

[light hearth]

but explain this part

[green linden]

I would divide the numerator by two to make things simpler so then i would have 2x^2+9x+15

[light hearth]

I don't think that'd be necessary, and honestly going further is dependent on how annoying your teacher wants to be on it

[green linden]

she wants the full solution and wants me to state the restrictions

[light hearth]

in terms of addition of algebraic fractions tho, your answer should be:

4x^2 + 18x + 30

(4x - 12)(6x + 6)

Right?

Unless you expanded out the denominator

if u did, then your denominator should be 24x^2 - 48x - 72

I think