Question

i need help simplifying

Answer 1

Do you know the answer? I think I have it, but I'm not sure if the calculations are completely correct.

Answer 2

no i dont, i have simplified the 10x^4 to equal 2x^2 and the 15x^2 to equal 3. thats as far as i got

Answer 3

I have \[2x^3+3x^2 \over 2(4x-3)\]

Answer 4

that is one of the options my question has. can you explain how you got that answer?

Answer 5

Yes. Let me write it down for you.

Answer 6

ok

Answer 7

\[{6x+9 \over 15x^2} \div {16x-12 \over 10x^4}\]
you can cancel the denominators as far as possible, since cross multiplying will make it so that you can. ----->\[{6x+9\over 3} \div {16x-12 \over 2x^2}\]

Answer 8

Do you get this so far?

Answer 9

After this, you can now factor the 6x-9 so that you can cancel out the 3.

\[{3(2x+3) \over 3} \div {16x-12 \over 2x^2}\]

Answer 10

\[(2x+3) \div {4(4x+3) \over 2x^2}\]

Answer 11

Now, you can cancel out the 2.

\[(2x+3) \div {2(4x+3) \over x^2}\]

Answer 12

Can you carry on from here, or should I show you the last steps?

Answer 13

dont you have to flip the 16x-12/2x^2 so that the 2x^2 is the numerator?

Answer 14

That's if you want to multiply straight instead of doing it at the end... You'd have to change the divide sign to the times sign.
eg ----->
\[(2x+3) \times {x^2 \over 2(4x+3)}\]

Answer 15

So, yes. You could do it like this, and now times the fractions. :) It would give you the same answer.

Answer 16

would it be easier to simplify everything then multiply?

Answer 17

For me, yes. And it can take less time, but if you're not used to it, then it might be easier to first multiply.

Answer 18

So, do you understand it now?

Answer 19

yeah a little more. can you show me how you got the final answer?

Answer 20

Sure.

Answer 21

Now, that it's flipped, you can easily just multiply the fractions ----->
\[2x^2(x+3) \over 2(4x-3)\]------->\[2x^3 +3x^2 \over 2(4x-3)\]----> Which is the final answer.

Answer 22

thank you!

Answer 23

Um hold on. I made a little mistake in explaning.

Answer 24

It should be \[x^2 \]not \[2x^2\]
and it should be (2x+3) not (x+3)

Answer 25

I just made that mistake in the last part. The other steps were correct :)

Answer 26

i like ur pic. @order