## angelwings996 2 years ago Algebra 2 help please!? Simplify the sum. State any restrictions on the variables.

1. angelwings996

2. Hero

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

3. angelwings996

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

4. phi

are you posting one of the multiple choices ?

5. angelwings996

This isn't a multiple choice problem

6. phi

you have the wrong sign on 5x

7. Hero

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

8. angelwings996

Okay, then what would I do?

9. phi

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

10. 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)

11. 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).

12. angelwings996

Okay, I get you so far

13. mathstudent55

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

14. angelwings996

Okay I did that

15. mathstudent55

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16. mathstudent55

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17. angelwings996

What did you do here?

18. 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.

19. angelwings996

Ohh okay

20. mathstudent55

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

21. mathstudent55

Now combine like terms on the numerator.

22. mathstudent55

Then try factoring the numerator.

23. angelwings996

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

24. mathstudent55

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

25. angelwings996

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

26. 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.

27. angelwings996

Okay, What would the restrictions be then ? @mathstudent55

28. angelwings996

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

29. 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.

30. angelwings996

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

31. angelwings996

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

32. mathstudent55

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

33. angelwings996

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