SOLUTION: I am confused about this problems. Multiply. (x^2)×(x^2+6x+9)/(x^2 9) (16x^3) Divide. (3y+12)÷(9y+36)/(8y^3)(16y^3) Perform the indicated operation. When no operation is in

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I am confused about this problems. Multiply. (x^2)×(x^2+6x+9)/(x^2 9) (16x^3) Divide. (3y+12)÷(9y+36)/(8y^3)(16y^3) Perform the indicated operation. When no operation is in      Log On


   

Question 251074: I am confused about this problems.
Multiply.
(x^2)×(x^2+6x+9)/(x^2 9) (16x^3)
Divide.
(3y+12)÷(9y+36)/(8y^3)(16y^3)
Perform the indicated operation. When no operation is indicated, simplify the ratinal expression completely.
(10m^4)×/(9a^2) (3a^2b)
(3x^2-5x)/(18x-30)
Thank you in advance
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
Multiply.
%28x%5E2%29%2A%28x%5E2%2B6x%2B9%29%2F%28x%5E2-9%29%2A%2816x%5E3%29
I assumed a minus sign between X^2 and 9 and then multiplication sign separating denominator fractions.
first, factor everything.
numerator is
x^2(x+3)(x+3).
denominator is
(x+3)(x-3)(16x^3).
together, we get
x%5E2%28x%2B3%29%28x%2B3%29 / %28x%2B3%29%28x-3%29%2816x%5E3%29
Now, we cancel: x=3 from top and bottom. X^2 from top and bottom. We get
%28x%2B3%29 / %28x-3%29%2816x%29
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Divide.
%283y%2B12%29%F7%289y%2B36%29/%288y%5E3%29%2816y%5E3%29
First step multiply by reciprocal:
%283y%2B12%29%2A%288y%5E3%29%2816y%5E3%29%2F%289y%2B36%29
Second step is to factor.
numerator becomes: 3%28y%2B4%29%2A8y%5E3%2A16y%5E3
denominator becomes: 9%28y%2B4%29
together we get:3%28y%2B4%29%2A8y%5E3%2A16y%5E3 / 9%28y%2B4%29
canceling the y+4 and the 3 with the 9, we get:
128y^6 / 3
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Perform the indicated operation. When no operation is indicated, simplify the rational expression completely.
(i) (10m^4)×/(9a^2) (3a^2b) -> I am not clear as to the x/ next to each other.
(ii) (3x^2-5x)/(18x-30)
step 1 - factor: x(3x-5) / 6(3x-5)
step 2 - reduce: x/6.