Question

Find the following difference.

Answer 1

\[\frac{ x+1 }{ x-6 }-\frac{ 3x+10 }{ 4x-24 }\]

Answer 2

The first step would be to make the denominators equal.

Answer 3

4(x-6)

Answer 4

Right, and multiply the numerator too. 4(x+1)

Answer 5

which numerator? second one?

Answer 6

well since you're multiplying the denominator of the first one by four, you need to make sure that the result of the multiplication is equal to what was before. So you're not really multiplying the denominator by four, but rather the whole fraction by one: or \[\frac{ 4 }{ 4 }\]

Answer 7

oh ok, so what about the 3x-10?

Answer 8

Let me redo that...the equation becomes\[\frac{ 4(x+1)-(3x+10) }{ 4x-24 }\]

Answer 9

Once the denominators are equal, it becomes a case of addition and subtraction.

Answer 10

Oh, i see...now what?

Answer 11

What answer did you come up with?

Answer 12

I didnt get there yet...so the denominator doesnt have to be factored?

Answer 13

You can factor it out, but it doesn't matter until we know what the numerator says. Once we know the numerator, then factoring the denominator matters.

Answer 14

In this instance, though, you will find that the numerator can cancel out something in the denominator.

Answer 15

the 4 & the 24 or the 4s?

Answer 16

Your solution should at the end look like:
\[\frac{ x-6 }{ 4(x-6) }\]
Is that what you got?

Answer 17

no lol

Answer 18

What did you get?

Answer 19

i didnt get anything, i was going with you, but my online work said that's incorrect...do the x-6s cancel out?

Answer 20

Yea, the final answer I have is 1/4

Answer 21

yaaaaaay !! thank you!

Answer 22

Do you understand everything/is everything OK?

Answer 23

yes, thank you very much