Question

How do I reduce this algebraic fraction https://unioncps.owschools.com/media/g_alg02_2013/5/172.gif

Answer 1

Take one expression at a time. All of them will need to be factored. The first term is 3a^2-13a+4. That will factor into (x+4)(x+1/3)

Answer 2

The denominator of that same fraction will factor into (x+1/3)(x+1/3)

Answer 3

The expression for the numerator in the second fraction is 7(4+a)

Answer 4

And the denominator of the second fraction factors to (a+4)(a-4)

Answer 5

So your whole mess looks like this now:\[\frac{ (x+4)(x+\frac{ 1 }{ 3 }) }{ (x+\frac{ 1 }{ 3 })(x+\frac{ 1 }{ 3 }) }\times \frac{ 7(4+a) }{ (a+4)(a-4) }\]

Answer 6

you will cancel out one of the (x+1/3)'s between the top and bottom of the first fraction, and then cancel out a (a+4) between the top and bottom of the second fraction like this:

Answer 7

Thanks so much!

Answer 8

\[\frac{ (x+4) }{ (x+\frac{ 1 }{ 3 }) }\times \frac{ 7 }{ (a-4) }\]That's all you can cancel. To simplify you will multiply straight across the top and straight across the bottom, like this:\[\frac{ 7(x+4) }{ (x+\frac{ 1 }{ 3 })(a-4) }\]

Answer 9

I am not sure if you need to distribute the 7 into the parenthesis on the top or FOIL out the bottom; it all depends upon what your textbook/teacher says about simplifying.