SOLUTION: Perform the indicated operatoin. When no operatoin is indicated, simplify the rational expression completely. 3x^2-5x/18x-30 (3x(squared)-5x over 18x-30)

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Perform the indicated operatoin. When no operatoin is indicated, simplify the rational expression completely. 3x^2-5x/18x-30 (3x(squared)-5x over 18x-30)      Log On


   

Question 621921: Perform the indicated operatoin. When no operatoin is indicated, simplify the rational expression completely.
3x^2-5x/18x-30
(3x(squared)-5x over 18x-30)
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
First, please put multiple term numerators and denominators in parentheses:
(3x^2-5x)/(18x-30)
It will make the problem clearer and clearer problems are more likely to get a quick response.

%283x%5E2-5x%29%2F%2818x-30%29
We could use long division for this. But first let's reduce the fraction, if possible. Reducing fractions is done by canceling factors that are common to the numerator and denominator. So we need to factor to see if there are factors to cancel. The GCF of the numerator is x and the GCF of the denominator is 6. Factoring these we get:
%28x%283x-5%29%29%2F%286%283x-5%29%29
As we can see, there is a factor common to the numerator and denominator: 3x-5. So we cancel them:
%28x%2Across%28%283x-5%29%29%29%2F%286%2Across%28%283x-5%29%29%29
leaving:
x%2F6
This, or since dividing by 6 is the same as multiplying by 1/6 are the same, %281%2F6%29x is the answer.