SOLUTION: Hi,I desperately need help with the following questions: 1. Square root n^2 + 12n + 36 2.Simplify the rational expression: x2 – 3x – 10 _____________ x2 – x – 20 3.

Algebra ->  Algebra  -> Square-cubic-other-roots -> SOLUTION: Hi,I desperately need help with the following questions: 1. Square root n^2 + 12n + 36 2.Simplify the rational expression: x2 – 3x – 10 _____________ x2 – x – 20 3.       Log On

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Question 196047: Hi,I desperately need help with the following questions:
1. Square root n^2 + 12n + 36
2.Simplify the rational expression:
x2 – 3x – 10
_____________
x2 – x – 20
3. Divide:
2x2 + 5x – 12 ÷ 2x2 – 7x + 6
______________ ________________
9x2 – 16 3x2 – x – 4
4. . Simplify:
√[144x^10y^12z^18]
5. Perform the indicated operations:
√[50] + 2√[32] – √[8]
6. Multiply:
(5√[2] + 2√[3])(√[2] – 2√[3])
7. Rationalize the denominator:
2____
√[6] – √[5]

Thanks a bunch



Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first three to get you started


# 1

sqrt%28n%5E2%2B12n%2B36%29=sqrt%28%28n%2B6%29%28n%2B6%29%29=sqrt%28%28n%2B6%29%5E2%29=abs%28n%2B6%29




# 2

%28x%5E2-3x-10%29%2F%28x%5E2-x-20%29 Start with the given expression.


%28%28x%2B2%29%28x-5%29%29%2F%28x%5E2-x-20%29 Factor x%5E2-3x-10 to get %28x%2B2%29%28x-5%29.


%28%28x%2B2%29%28x-5%29%29%2F%28%28x%2B4%29%28x-5%29%29 Factor x%5E2-x-20 to get %28x%2B4%29%28x-5%29.


%28%28x%2B2%29highlight%28%28x-5%29%29%29%2F%28%28x%2B4%29highlight%28%28x-5%29%29%29 Highlight the common terms.


%28%28x%2B2%29cross%28%28x-5%29%29%29%2F%28%28x%2B4%29cross%28%28x-5%29%29%29 Cancel out the common terms.


%28x%2B2%29%2F%28x%2B4%29 Simplify.


So %28x%5E2-3x-10%29%2F%28x%5E2-x-20%29 simplifies to %28x%2B2%29%2F%28x%2B4%29.


In other words, %28x%5E2-3x-10%29%2F%28x%5E2-x-20%29=%28x%2B2%29%2F%28x%2B4%29 where x%3C%3E-4 or x%3C%3E5




# 3



%28%282x%5E2%2B5x-12%29%2F%289x%5E2-16%29%29%2F%28%282x%5E2-7x%2B6%29%2F%283x%5E2-x-4%29%29 Start with the given expression.


%28%282x%5E2%2B5x-12%29%2F%289x%5E2-16%29%29%28%283x%5E2-x-4%29%2F%282x%5E2-7x%2B6%29%29 Multiply the first fraction %282x%5E2%2B5x-12%29%2F%289x%5E2-16%29 by the reciprocal of the second fraction %282x%5E2-7x%2B6%29%2F%283x%5E2-x-4%29.


%28%28%28x%2B4%29%282x-3%29%29%2F%289x%5E2-16%29%29%28%283x%5E2-x-4%29%2F%282x%5E2-7x%2B6%29%29 Factor 2x%5E2%2B5x-12 to get %28x%2B4%29%282x-3%29.


%28%28%28x%2B4%29%282x-3%29%29%2F%28%283x-4%29%283x%2B4%29%29%29%28%283x%5E2-x-4%29%2F%282x%5E2-7x%2B6%29%29 Factor 9x%5E2-16 to get %283x-4%29%283x%2B4%29.


%28%28%28x%2B4%29%282x-3%29%29%2F%28%283x-4%29%283x%2B4%29%29%29%28%28%28x%2B1%29%283x-4%29%29%2F%282x%5E2-7x%2B6%29%29 Factor 3x%5E2-x-4 to get %28x%2B1%29%283x-4%29.


%28%28%28x%2B4%29%282x-3%29%29%2F%28%283x-4%29%283x%2B4%29%29%29%28%28%28x%2B1%29%283x-4%29%29%2F%28%282x-3%29%28x-2%29%29%29 Factor 2x%5E2-7x%2B6 to get %282x-3%29%28x-2%29.


%28%28x%2B4%29%282x-3%29%28x%2B1%29%283x-4%29%29%2F%28%283x-4%29%283x%2B4%29%282x-3%29%28x-2%29%29 Combine the fractions.


%28%28x%2B4%29highlight%28%282x-3%29%29%28x%2B1%29highlight%28%283x-4%29%29%29%2F%28highlight%28%283x-4%29%29%283x%2B4%29highlight%28%282x-3%29%29%28x-2%29%29 Highlight the common terms.


%28%28x%2B4%29cross%28%282x-3%29%29%28x%2B1%29cross%28%283x-4%29%29%29%2F%28cross%28%283x-4%29%29%283x%2B4%29cross%28%282x-3%29%29%28x-2%29%29 Cancel out the common terms.


%28%28x%2B4%29%28x%2B1%29%29%2F%28%283x%2B4%29%28x-2%29%29 Simplify.


%28x%5E2%2B5x%2B4%29%2F%283x%5E2-2x-8%29 FOIL.


So %28%282x%5E2%2B5x-12%29%2F%289x%5E2-16%29%29%2F%28%282x%5E2-7x%2B6%29%2F%283x%5E2-x-4%29%29 simplifies to %28x%5E2%2B5x%2B4%29%2F%283x%5E2-2x-8%29.


In other words, %28%282x%5E2%2B5x-12%29%2F%289x%5E2-16%29%29%2F%28%282x%5E2-7x%2B6%29%2F%283x%5E2-x-4%29%29=%28x%5E2%2B5x%2B4%29%2F%283x%5E2-2x-8%29 where x%3C%3E-4%2F3, x%3C%3E4%2F3, x%3C%3E3%2F2, or x%3C%3E2