Question

Perform operations

Answer 1

\[\frac{ 9x }{ x-5 }+\frac{ 7x }{ 5-x }+\frac{ 9x-1 }{ x^2-25 }\]

Answer 2

You can do this to the 2nd denominator
5 - x = -(-5 + x) = -(x - 5)
so now you have the same denominator in the first two expression and can combine
\[\frac{ 9x }{ x-5 }-\frac{ 7x }{ x-5 }+\frac{ 9x-1 }{ x^2-25 }\]
\[\frac{ 2x }{ x-5 }+\frac{ 9x-1 }{ x^2-25 }\]

Answer 3

now you need a common denominator between (x - 5) and (x² - 5). Any ideas on how to get that?

Answer 4

(x^2-25) = (x+5)(x-5)

Answer 5

First you need a COMMON denominator @savy :)

Answer 6

Recognizing the difference of two squares may come in handy later though.

Answer 7

Recall you can multiply the numerator and denominator of a fraction by any nonzero number.

For example,
$$\large \dfrac{2}{3} = \dfrac{2•2}{2•3} = \dfrac{4}{6}$$


Read as 2 is to 3 as 4 is to 6.

Answer 8

@skullpatrol i think using the difference of two squares is helpful to see how to get the common denominator. Helps to see what is "missing".

Answer 9

So the common denominators are x-5 and x+5, right?

Answer 10

Good point @agent0smith

Answer 11

The common denominator is (x-5)(x+5) @savy it is one number common to both fractions.

Answer 12

that's what i said before..

Answer 13

Where?

Answer 14

@Savy "common denominators are x-5 and x+5"

that is not at all the same as saying the common denominator is (x-5)(x+5)

Answer 15

technically it is...

Answer 16

How so?

Answer 17

No @Savy it really is not. You have to write things in a mathematically correct way, so that others can understand them.

Answer 18

"Common" means ONE or more things shared between two things, right?

Answer 19

How are we supposed to know x-5 and x+5 doesn't mean (x-5) + (x+5)?