Question

divide and simplify to lowest terms

3y+5/6y+1 + 3y+5/y+6

Answer 1

Starting with the form \[\frac{3y+5}{6y+1}+\frac{3y+5}{y+6}\]
We multiply each expression by the conjugate of the other's denominator. For instance:

For \[\frac{3y+5}{6y+1}\]We multiply by \[\frac{y+6}{y+6}\]
We can do this because that expression equals 1. By doing this to both sides, we end up with a common denominator used to add the fractions. In full:
\[\frac{3y+5}{6y+1}(\frac{y+6}{y+6})+\frac{3y+5}{y+6}(\frac{6y+1}{6y+1})\]
It looks a bit ugly, but through distribution we get
\[\frac{3y^2+23y+30}{6y^2+37y+6}+\frac{18y^2+33y+5}{6y^2+37y+6}\]
Still ugly, but with equivalent denominators, we can add to get
\[\frac{21y^2+56y+35}{6y^2+37y+6}\]
Go ahead and factor out a 7 on top
\[7\frac{3y^2+8y+5}{6y^2+37y+6}\]
And then factor back out, since we can't cancel anything.
\[7\frac{(y+1)(3y+5)}{(y+6)(6y+1)}\]
I'm not a big fan of these problems either, don't worry

Answer 2

idk why it's telling me its wrong. thats strange ugh i really do hate these problems

Answer 3

,...?

Answer 4

it says simplify AND type in factored form

Answer 5

I'm thinking about it...if you wanted to separate them all out, you could get to
\[\frac{9}{2 (6 y+1)}-\frac{13}{y+6}+\frac{7}{2}\]

Answer 6

it said correct answer was y+6/6y+1

Answer 7

unless the form you typed originally is wrong, that's not possible. One of the two would need to be reciprocated

Answer 8

i copyed and pasted over idk want to try a different one? please

Answer 9

yeah sure