Division with algebra fractions: (28x+14)/(45x-30) // (14x+7

[Texter]

Hey. I've never had algebra in high school and I managed to get into a intermediate algebra class in college. I should really say that I am stuck on a step in multiplications of fractions. I've worked out a problem and am stuck on the step.

28x+14 14x+7
-------- / -------
45x-30 30x-20

Okay, I know the second fraction I need to reverse it and cancel out what I can.

28x+14 30x-20
-------- . --------
45x-30 14x+7


2+2 2-2
----- . -----
3-3 1+1

And now i'm stuck... I'm trying to figure out if I take the sum of 2+2 and multiply it by the remainder of 2-2 and the same thing with the denominator.

 

[galactus]

\(\displaystyle \L\\\frac{(28x+14)}{(45x-30)}\cdot\frac{(30x-20)}{(14x+7)}\)

Factor:

\(\displaystyle \L\\\frac{14(2x+1)}{15(3x-2)}\cdot\frac{10(3x-2)}{7(2x+1)}\)

Cancel:

\(\displaystyle \L\\\frac{14\sout{(2x+1)}}{15\sout{(3x-2)}}\cdot\frac{10\sout{(3x-2)}}{7\sout{(2x+1)}}\)

You're left with:

\(\displaystyle \L\\\frac{\sout{14}^{2}}{\sout{15}^{3}}\cdot\frac{\sout{10}^{2}}{\sout{7}^{1}}\)

\(\displaystyle \L\\\frac{2}{3}\cdot\frac{2}{1}=\frac{4}{3}\)

 

[Texter]

Boy, that helped out alot. I'm going to write that down in my notes.

To multiply.

1. Factor
2. Cancel

Thanks alot!