Question

Can someone please help me with this math question?
Please? I will fan and give a medal!!

Answer 1

Please help me to simplify this rational expression -
(x^2-7x+10) (7x
----------- * ------
(7x-35) (x-2)

Answer 2

once again - start by multiplying. What do you get as a product?

Answer 3

also - don't multiply in/distribute the 7x on the top yet! leave everything as it, just smoosh them together.

Answer 4

(x^2-7x+10)(7x)
--------------------
(7x-35)(x-2)
Put it like this right?

Answer 5

yep! Now look for terms you can break down more - like the 7x-35 on the bottom. How can we simplify that?

Answer 6

Would I subtract 7x-35? Which = 28

Answer 7

no - 7 is a factor in both terms. Divide both by 7

Answer 8

\[\frac{(x-5)(x-2)}{7(x-5)}\times \frac{7x}{x-2}\]

Answer 9

Cancel the common factors

Answer 10

You will see that the result is simply "x"

Answer 11

do you want help with factoring and simplifying further? or do you feel ok and able to follow mertsj's answer?

Answer 12

Umm if @Mertsj could explain the steps that he/she did then I'll be ok following them but right now I don't understand what he is doing

Answer 13

we'll work on factoring, it's ok
do you understand the 7(x-5) part? we can tackle the other one if you do

Answer 14

Would you mind explaining it?

Answer 15

sure!

When you divide the (7x-35) by 7, you divide each term separately - so you wind up with (7/7)x - (35/7) - which ends up being 7(x-5).

The 7 stays out front to make sure you know it's been taken out already, and then you put the quotients inside (x and -5).

Make sense now?

Answer 16

Yes sir it does!

Answer 17

perfect! let's move on to the scarier looking one. How do you normally factor polynomials? Do you use the box method (I find it to be the easiest!)

Answer 18

I honestly never heard of the box method, but I won't mind trying it!

Answer 19

ok. Draw a square, and then put a cross in the middle. Like this :

Answer 20

In the top left, write the coefficient of the x^2 term (one, in this case). In the bottom right, write the coefficient of the constant term (10, in this case)

Answer 21

(another way to do it includes the x^2 - I'll include it in brackets. It's not necessary, as long as you know it's there.) you should have something that looks like this :

Answer 22

Okay got it!

Answer 23

what you do from here is you multiply the two together - this is in case you have a coefficient in front of the x^2 term. Not applicable in this case!

So what we want to do from here is find 2 numbers that add up to -7, and multiply for 10. List the factors of 10 beside the box.

Answer 24

note : Signs are important! -1 and -10 are a pair of factors, as are 1 and 10 - and it matters which ones you pick!

Answer 25

Ok

Answer 26

which pair of factors will add up to -7?

Answer 27

I'm trying to think of that, I'm not too good with negatives.

Answer 28

that's ok.

The list of factors should be :
-1 -10
-2 -5
2 5
1 10

-2 + -5 = -7, so those are the ones we'll go with. Now we need to update the box.

Put -2x and -5x in the open boxes - it doesn't matter which ones, as long as they aren't already filled and they both make it in. You should wind up with something like :