Question

Divide: (7a+28)/(a-4) ÷ (a^2+9-12)/14a

Answer 1

To divide two fractions, multiply the first one by the reciprocal of the second one.
First, rewrite the first fraction, then a multiplicatin sign, then flip the second fraction.
Next step is factor every numerator and denominator that is factorable.

Answer 2

\[\frac{ 7a+28 }{ a-4 }\times \frac{ 14a }{ a^2+0-12 } this?\]

Answer 3

Yes, but check your original denominator of the second fraction and here again. Did you leav an "a" out?

Answer 4

I meant the original numerator of the second fraction, which became the denominator after flipping.

Answer 5

\[\frac{ 7a+28 }{ a-4} \times \frac{ 14a }{ a^2+9-12 }\] I put 0 instead of 9

Answer 6

Is it just 9 or 9a?

Answer 7

just 9

Answer 8

Your original posting may have been copied incorrectly.

Answer 9

wait, yea its just "a" no nine at all... my eyes failed me at the moment

Answer 10

Ok

Answer 11

\[\frac{ 7a+28 }{ a-4 }\times \frac{ 14a }{ a^2+a-12 }\]

Answer 12

Great. Now factor everything that can be factored.
Can you factor 7a + 28? Look for the greatest common factor between 7a and 28.

Answer 13

7 so its be a and 4 instead?

Answer 14

it'd* miss spell

Answer 15

\[\frac{ a+4 }{ a-4 }\times \frac{ 14a }{ a^2+a-12 }\]

Answer 16

Yes, 7 is the factor, but you still need to write it as 7(a + 4)

Answer 17

Then a - 4 in the denominator can't be factored, so it stays as it is.
Next is 14a, which also can't be factored, so it stays as it is.
Finally there is a^2 + a - 12 which can be factored.
Do you know how to factor a^2 - a + 12?

Answer 18

Does it have to do with a? I mean can you use a to factor it?

Answer 19

To factor a trinomial of the type: x^2 + ax + b, such as a^2 + a - 12,
come up with two numbers that multiply to b and add to a. In your case, you need
two numbers that multiply to -12 and add to 1.

Answer 20

-3 and 4

Answer 21

So far we have this, and we are working on the second denominator.
\[\frac{ 7(a + 4) }{ a - 4 } \times \frac{ 14a }{ a^2 + a - 12 } \]

Answer 22

Correct. Now that you have the 2 numbers, all you do is:
a^2 + a - 12 = (a - 3)(a + 4)
That's how it's factored. (a - 3)(a + 4) now goes in the second denominator.

Answer 23

\[\frac{ 7(a + 4) }{ a - 4 } \times \frac{ 14a}{ (a - 3)(a + 4) } \]

Answer 24

To multiply two fractions together, you multiply the two numerators together, and you multiply the two denominators together.

Answer 25

\[\frac{ 7(a+4)\times 14a }{ a-4\times(a-3)(a+4) }\]

Answer 26

and the a+4's cancel out?

Answer 27

\[\frac{ 7(a + 4)(14a) }{ (a - 4)(a - 3)(a + 4) }\]

Answer 28

You are correct, except you need parentheses around the a - 4.
You are also correct that the a + 4 terms cancel out.

Answer 29

\[\frac{ 7(14a) }{ (a-4)(a-3) } \] so this is what is left?

Answer 30

Yes. Now you can multiply together 7 and 14a and get 98a. You can leave the denominator factored as it is.

Answer 31

\[\frac{ 98a }{ (a-4)(a-3) }\]

Answer 32

You got it! Good job!

Answer 33

Thank you for helping!

Answer 34

wlcm