## Subtracting Rational Expressions

Simplificatation, evaluation, linear equations, linear graphs, linear inequalities, basic word problems, etc.

### Subtracting Rational Expressions

Hi New Here and new to the college math. I have started back to school after 43 yrs and this is like a foreign language to me so I am hoping I can get an explaination I can understand and use.

Subtract:

_____1_____ minus ____x+4______
x^2 - 16 minus x^2 - 3x - 4

Thank you for your time. Can't figure out how to type this problem out better so I hope you get the gist of it.
Shari1948
shari1948

Posts: 5
Joined: Tue Jul 14, 2009 5:10 am

shari1948 wrote:Can't figure out how to type this problem out better....

To learn how to format, please follow the link you saw in the "How to type math clearly" article when you "review[ed] the Forum Rules before posting".

shari1948 wrote:Subtract:

_____1_____ minus ____x+4______
x^2 - 16 minus x^2 - 3x - 4

I believe the expression is meant to be as follows:

. . . . .$\frac{1}{x^2\, -\, 16}\, -\, \frac{x\, +\, 4}{x^2\, -\, 3x\, -\, 4}$

The first step is to factor the denominators, to find what your common denominator will be. How far have you gotten on this step?

Thank you!

stapel_eliz

Posts: 1706
Joined: Mon Dec 08, 2008 4:22 pm

### Re: Subtracting Rational Expressions

Thank you for the link I will study it before I post a problem again.

I have figured that 4 is the common denominator ie (x +4)(x-4), but when I get into the subtraction of this I find that someplace there is (x+1) that I have no idea where it came from. Then the signs change and I don't know where or why.

Thank you again for the promt reply

Shari
shari1948

Posts: 5
Joined: Tue Jul 14, 2009 5:10 am

shari1948 wrote:I have figured that 4 is the common denominator ie (x +4)(x-4)...

When the factors of the denominators are x + 4, x - 4, x + 1, how are you getting a common denominator of just the number "4"?

shari1948 wrote:...but when I get into the subtraction of this...

What are you subtracting?

To learn how to factor quadratics, try here. To learn how to convert rational expressions (that is, polynomial fractions) to common denominators and then how to add and subtract them, try here.

Then please attempt the exercise, starting from the first step, being the factorization of the denominators:

. . . . .$\frac{1}{(x\, -\, 4)(x\, +\, 4)}\, -\, \frac{x\, +\, 4}{(x\, -\, 4)(x\, +\, 1)}$

stapel_eliz

Posts: 1706
Joined: Mon Dec 08, 2008 4:22 pm

### Re: Subtracting Rational Expressions

Thank you again. I will give the links are serious read and hopefully something will click. The "4" is my mind set of math from years back. I know that 16 can be divided by 4 and 4 x 4 is 16 and -4 x 4 is -16. Now to get a grip on all this factoring.

Shari
shari1948

Posts: 5
Joined: Tue Jul 14, 2009 5:10 am

### Re: Subtracting Rational Expressions

$(x+1) - (x+4)$
________________________
$(x+4)(x-4) - (x-4)(x+1)$

Now is when the lack of understand arises. The instructor gave us the answer, but I can't figure out what I am missing to get the answer she gave. I feel I am missing something in numorator and I am so confused still.

The answer is according to the instuctor:

$-x^2 - 7x - 16$
____________________
$(x+4) (x-4) (x-1)$

I am lost as to where the (x-1) came from
shari1948

Posts: 5
Joined: Tue Jul 14, 2009 5:10 am

Following the steps outlined in the lesson, provided earlier:

What did you get when you converted the two fractions to their common denominator?

What did you get when you multiplied out the numerators?

What did you get when you then, only at that stage, combined the (now "like") fractions, subtracting the one numerator from the other?

What did you get when you simplified this subtraction?

Please show your steps, so we can see where you're having trouble. (And re-read the lesson, as needed.)

Thank you!

stapel_eliz

Posts: 1706
Joined: Mon Dec 08, 2008 4:22 pm

### Re: Subtracting Rational Expressions

I think I have this figured out. I don't get this posting on this site so am having a hard time showing my work with the text so here is the other way.

1 (x+1) -- x+4 (x -4)
____________________
(x+4)(x+4) (x+1) -- (x+1)(x-4)(x+4)

(x+1) -- (x^2 + 8x + 16)
____________________
(x-4)(x+4)(x+1)

I changed the signs when I dropped the ()
-x^2 - 7x -15

Then subtracted.

Thanks again for the help and I will be thankful when this is correctly done

Shari
shari1948

Posts: 5
Joined: Tue Jul 14, 2009 5:10 am