SOLUTION: how would i do this? Simplify the following fractions by putting them in lowest terms or by performing the indicated operations 81-x to the 4th over 3-x divided by 9+x2 over 9 =

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: how would i do this? Simplify the following fractions by putting them in lowest terms or by performing the indicated operations 81-x to the 4th over 3-x divided by 9+x2 over 9 =      Log On


   

Question 146834: how would i do this? Simplify the following fractions by putting them in lowest terms or by performing the indicated operations
81-x to the 4th over 3-x divided by 9+x2 over 9 =
Answer by mangopeeler07(462) About Me  (Show Source):
You can put this solution on YOUR website!
Start with %2881-x%5E4%29%2F%283-x%29 divided by %289%2Bx%5E2%29%2F%289%29.

Find the common denominator, which would be 9(3-x). Manipulate the fractions and get %289%2881-x%5E4%29%29%2F9%283-x%29 divided by %28%283-x%29%289%2Bx%5E2%29%29%2F%289%283-x%29%29.

Then eliminate the denominators from the equation. Get 9%2881-x%5E4%29 divided by %283-x%29%289%2Bx%5E2%29.

Factor all of the expressions. The expression 81-x%5E4 factors into %289%2Bx%5E2%29%289-x%5E2%29. Then 9-x%5E2 factors to %283-x%29%283%2Bx%29. So the numerator becomes 9%289%2Bx%5E2%29%283-x%29%283%2Bx%29 while the denominator remains %289%2Bx%5E2%29%283-x%29. So it looks like: %289%289%2Bx%5E2%29%283-x%29%283%2Bx%29%29%2F%28%289%2Bx%5E2%29%283-x%29%29.

Now just cancel out like terms in the numerator and the denominator, which would be %283-x%29 and %289%2Bx%5E2%29. Then you are left with %289%283%2Bx%29%29%2F1. or 9%283%2Bx%29. You can stop there if you want to. Going further is not necessary, but if you want to anyway, read on.

It is very easy from here. Just distribute the 9 to both terms and get %2827%2B9x%29%2F1 or simply 27%2B9x.