Algebra 2 help please!?
Simplify the sum. State any restrictions on the variables.

- angelwings996

Algebra 2 help please!?
Simplify the sum. State any restrictions on the variables.

- katieb

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- angelwings996

##### 1 Attachment

- Hero

Hint: Multiply the first fraction by (x - 3)/(x-3)

- angelwings996

so would it become \[\frac{ x ^{2} + 5x + 6 }{ x ^{2} - 9 }\] @Hero

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## More answers

- phi

are you posting one of the multiple choices ?

- angelwings996

This isn't a multiple choice problem

- phi

you have the wrong sign on 5x

- Hero

Actually the numerator should be x^2 - 5x + 6

- angelwings996

Okay, then what would I do?

- phi

once you have a common denominator, you can combine the tops

- mathstudent55

Since you are adding fractions, you need a common denominator.
The denominator of the left fraction is simply x + 3.
You need to factor the denominator of the right fraction.
x^2 - 9 = (x + 3)(x - 3)

- mathstudent55

Since the right denominator has factors (x + 3)(x - 3) and the left fraction only has
(x + 3), you need to multiply the numerator and denominator of the left fraction by
(x - 3).

- angelwings996

Okay, I get you so far

- mathstudent55

Then multiply out the numerator of the left fraction (x + 3)(x - 2)

- angelwings996

Okay I did that

- mathstudent55

|dw:1359654823726:dw|

- mathstudent55

|dw:1359654885990:dw|

- angelwings996

What did you do here?

- mathstudent55

Since both fractions now have the same denominator, you can write them as a single fraction over the common denominator.
Now combine like terms in the numerator.

- angelwings996

Ohh okay

- mathstudent55

I multiplied out the left numerator and I added the right numerator, and set the whole thing over the common denominator.

- mathstudent55

Now combine like terms on the numerator.

- mathstudent55

Then try factoring the numerator.

- angelwings996

When I combine like terms I got \[\frac{ x ^{2} + 11x - 6 }{ (x+3)(x-3) }\]

- mathstudent55

Correct. The last step is to try to factor the numerator to see if you can simplify the fraction.

- angelwings996

I can't figure out how to factro this, nothing I can find will come up with both 11 and 6

- mathstudent55

This kind of factoring involves finding two numbers that multiply to -6 and add to 11. There aren't any, so it can't be factored, and the addition is finished.

- angelwings996

Okay, What would the restrictions be then ? @mathstudent55

- angelwings996

Would the answer be with the denominator factored or can I put x^2 - 9 ?

- mathstudent55

The restrictions are any values of x that would make the denominator zero. Since the denominator is x^2 - 9 which you know factors into (x + 3)(x - 3), set
x + 3 = 0 and solve for x
and set
x - 3 = 0 and solve for x.
Those two x values are the restrictions.

- angelwings996

Okay thank you..so the answer woould be \[\frac{ x ^{2} + 11x - 6 }{ (x + 3)(x - 3) } ; x \neq -3, 3\] @mathstudent55

- angelwings996

Or would I put x^2 - 9 as the denominator ?

- mathstudent55

You can leave the denominator factored. It's perfectly acceptable. It's also fine to multiply it out. Either way is good.

- angelwings996

Okay, thank you so much for your help ! (:

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