Question

what is the simplified form of (3 / 4x+3) + (21 / 8x^2-14x-15) ? Help!

Answer 1

Ok. For this, you have to factor the \(8x^2 - 14x - 15\). Do you know how to do that?

Answer 2

not when the first and last numbers dont have factors that end up equaling -14

Answer 3

Find factors of -120 that add up to -14. How about -20 and 6?

Answer 4

So:
\[8x^2 - 14x - 15 \rightarrow 8x^2 - 20x + 6x - 15 \rightarrow (8x^2 - 20x) + (6x - 15) \rightarrow ?\]

Answer 5

ohhh okay

Answer 6

Tell me what you get.

Answer 7

6(2x+5) / (2x-5)(4x+3)

Answer 8

Yup. Now back to the original problem.
\[\frac{3}{4x + 3} + \frac{21}{(2x - 5)(4x + 3)}\rightarrow \frac{3}{4x + 3} \times \frac{2x - 5}{2x - 5}+ \frac{21}{(2x - 5)(4x + 3)}\]Can you try to do the rest?

Answer 9

Its all on paper

Answer 10

its alot is there like a way i can send a picture?

Answer 11

wait so 6(2x+5) / (2x-5)(4x+3) isnt the final answer??

Answer 12

No.
\[\frac{3}{4x + 3} \times \frac{2x - 5}{2x - 5}+ \frac{21}{(2x - 5)(4x + 3)} \rightarrow \frac{3(2x - 5) + 21}{(2x - 5)(4x + 3)}\]Think you can finish what's in the numerator?

Answer 13

\[\frac{6x - 6}{(2x - 5)(4x + 3)}\]That's what the end result is.

Answer 14

Do you get it?

Answer 15

ya but wouldnt it be 6x+1 / (2x-5)(4x+3) ?

Answer 16

No. 3(2x - 5) = 6x - 15. THen, there's the + 21. 21 - 15 = 6 See?

Answer 17

yeah that makes sense but the workbook says a.) 6(2x+5) / (2x-5)(4x+3)
b.) 6/ 4x+3
c.) 6x+1 / (2x-5)(4x+3)
d.) 6x+1 / (2x+5)(4x+3)
are the only options

Answer 18

I don't see how you can get any of those...

Answer 19

This is the only thing that I can see possible...
\[\frac{6(x + 1)}{(2x - 5)(4x + 3)}\]

Answer 20

yeah thats what i thought too. Oh well

Answer 21

Sorry I can't be of more help...

Answer 22

@ganeshie8 Do you see my mistake anywhere?

Answer 23

No. looks perfect to me. and wolfrom confirms the same :)

http://www.wolframalpha.com/input/?i=+%283+%2F+%284x%2B3%29%29+%2B+%2821+%2F%28+8x%5E2-14x-15%29%29

Answer 24

must be printing mistake in the options...

Answer 25

thats so weird! at least i know how to do it, thanks guys :)

Answer 26

Alright. np :) And thanks ganeshie8