Question

simplify the complex fraction

Answer 1

\[\frac{ \frac{ n-6 }{ n^2+11n+24 } }{ \frac{ n+1 }{ n+3 }}\]

Answer 2

You call that complex? Pffft! :-)

Answer 3

Okay, first thing I would do is factor anything that can be factored. What might that be here?

Answer 4

after you factor it you get the equation \[\frac{ \frac{ n-6 }{ (n+8)(n+3) } }{ \frac{ n+1 }{ n+3 } }\]

Answer 5

right??

Answer 6

We're going to be optimistic that we'll be able to cancel something out and make our job a bit simpler.

Good, that's the correct factoring.

Next, take the denominator fraction, flip it upside down, and multiply it with the numerator fraction. Remember, dividing by a fraction is equivalent to multiplying by the reciprocal of the fraction.

Answer 7

\[\frac{\frac{a}b } {\frac{c}d } = \frac{a}b * \frac{d}c\]

Answer 8

ok give me a second and i will try

Answer 9

ok how do we multiply that??

Answer 10

n-6 times n+3

Answer 11

\[\frac{(n-6)}{(n+8)(n+3)}*\frac{(n+3)}{(n+1)}\]See anything to cancel?

Answer 12

n+3

Answer 13

Okay, what do you get after you do that?

Answer 14

so that leaves us with \[\frac{ n-6 }{ (n+8)(n+1) }\]

Answer 15

Yes. I'd probably leave it there, but you could expand the denominator to \[\frac{(n-6)}{(n^2+9n+8)}\]

Answer 16

thats our answer isnt it

Answer 17

i have a random question. well it goes with the next question im stuck on what is a direct variation or a inverse variation??