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

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Hero
 2 years ago
Best ResponseYou've already chosen the best response.1Hint: Multiply the first fraction by (x  3)/(x3)

angelwings996
 2 years ago
Best ResponseYou've already chosen the best response.0so would it become \[\frac{ x ^{2} + 5x + 6 }{ x ^{2}  9 }\] @Hero

phi
 2 years ago
Best ResponseYou've already chosen the best response.0are you posting one of the multiple choices ?

angelwings996
 2 years ago
Best ResponseYou've already chosen the best response.0This isn't a multiple choice problem

phi
 2 years ago
Best ResponseYou've already chosen the best response.0you have the wrong sign on 5x

Hero
 2 years ago
Best ResponseYou've already chosen the best response.1Actually the numerator should be x^2  5x + 6

angelwings996
 2 years ago
Best ResponseYou've already chosen the best response.0Okay, then what would I do?

phi
 2 years ago
Best ResponseYou've already chosen the best response.0once you have a common denominator, you can combine the tops

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.1Since 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
 2 years ago
Best ResponseYou've already chosen the best response.1Since 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
 2 years ago
Best ResponseYou've already chosen the best response.0Okay, I get you so far

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.1Then multiply out the numerator of the left fraction (x + 3)(x  2)

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1359654823726:dw

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1359654885990:dw

angelwings996
 2 years ago
Best ResponseYou've already chosen the best response.0What did you do here?

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.1Since 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.

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.1I multiplied out the left numerator and I added the right numerator, and set the whole thing over the common denominator.

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.1Now combine like terms on the numerator.

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.1Then try factoring the numerator.

angelwings996
 2 years ago
Best ResponseYou've already chosen the best response.0When I combine like terms I got \[\frac{ x ^{2} + 11x  6 }{ (x+3)(x3) }\]

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.1Correct. The last step is to try to factor the numerator to see if you can simplify the fraction.

angelwings996
 2 years ago
Best ResponseYou've already chosen the best response.0I can't figure out how to factro this, nothing I can find will come up with both 11 and 6

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.1This 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
 2 years ago
Best ResponseYou've already chosen the best response.0Okay, What would the restrictions be then ? @mathstudent55

angelwings996
 2 years ago
Best ResponseYou've already chosen the best response.0Would the answer be with the denominator factored or can I put x^2  9 ?

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.1The 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
 2 years ago
Best ResponseYou've already chosen the best response.0Okay thank you..so the answer woould be \[\frac{ x ^{2} + 11x  6 }{ (x + 3)(x  3) } ; x \neq 3, 3\] @mathstudent55

angelwings996
 2 years ago
Best ResponseYou've already chosen the best response.0Or would I put x^2  9 as the denominator ?

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.1You can leave the denominator factored. It's perfectly acceptable. It's also fine to multiply it out. Either way is good.

angelwings996
 2 years ago
Best ResponseYou've already chosen the best response.0Okay, thank you so much for your help ! (:
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