Question

Add or subtract as indicated. Simplify the results if possible.

2x^2/x-5 - 25+x^2/x-5 =

Answer 1

Is this simplifying an expression or solving this for x?

Answer 2

They each ask for two very different things.

Answer 3

simplifying expression

Answer 4

Ok, that means that when you simplify this, you will still have a fraction, but the goal here is to make both denominators the same.

Answer 5

It appears that they are both x - 5.

Answer 6

That is really good. Now we can just simplify the numerators. That would look like this, put all over the common denominator.

Answer 7

\[\frac{ 2x ^{2}-(25+x ^{2} )}{ x-5 }\]

Answer 8

yup

Answer 9

now we factor 25 + x^2

Answer 10

The only tricky part here is that you have to change the +x^2 into a - x^2 because of the negative sign in between the two original fractions. That would look like this, simplified:

Answer 11

\[\frac{ x ^{2}-25 }{ x-5 }\]

Answer 12

This is what you have to factor now. My answer is kind of different from yours; you have 25 + x^2, when it is actually x^2 - 25, which is the difference of two perfect squares.

Answer 13

correct

Answer 14

and tahat can be simplified to (x-5) and (x+5)

Answer 15

that*

Answer 16

Well, DawnR, I was hoping he/she could come up with it himself/herself, but oh well....thanks for giving the answer.

Answer 17

it's not the answer he/she still has one more step to finish it :p

Answer 18

But factoring is a huge part of coming to that correct answer. Right?

Answer 19

but it doesn't count as an answer :)

Answer 20

What do you get, moiz41510?

Answer 21

\[2x ^{2} - (x+5)(x-5) / (x-5)\]

Answer 22

No; the 25 + x^2 does not factor like that at all. Only the difference of two squares factors like that.

Answer 23

see i didn't tell her/him the answer :D

Answer 24

ahh

Answer 25

sorry

Answer 26

Before simplifying you get \[\frac{ 2x ^{2}-25-x ^{2} }{ x-5 }\]

Answer 27

You subtract like this:\[\frac{ 2x ^{2}-x ^{2}-25 }{ x-5 }\]to get this\[\frac{ x ^{2} -25}{ x-5 }\]See? Don't be sorry!

Answer 28

Now the numerator is the difference of two perfect squares. Can you factor that now?

Answer 29

what happened to the 2x^2?

Answer 30

You subtracted 2x^2 - x^2 to get x^2. Look above to my equations.

Answer 31

The x^2 terms combine because they are like terms.

Answer 32

ok got it

Answer 33

Just like 2x - x = x, it's the same thing with the x^2 terms. The x^2 terms combine: subtract 1x^2 from 2x^2 and get 1x^2 left over.

Answer 34

Now can you factor the numerator?

Answer 35

X+5!!

Answer 36

YES!!!!!!!!!!!!!!!!!!!!!!!!!

Answer 37

thankyou so much!