SOLUTION: Please help me solve this: {{{(12x^2)/(3x^2+12x)}}} divided by {{{(4x^3-36x)/(x^2+x-12)}}}

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Please help me solve this: {{{(12x^2)/(3x^2+12x)}}} divided by {{{(4x^3-36x)/(x^2+x-12)}}}      Log On


   

Question 78331: Please help me solve this:
%2812x%5E2%29%2F%283x%5E2%2B12x%29 divided by %284x%5E3-36x%29%2F%28x%5E2%2Bx-12%29
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28%2812x%5E2%29%2F%283x%5E2%2B12x%29%29%2F%28%284x%5E3-36x%29%2F%28x%5E2%2Bx-12%29%29 Start with the given expression

%28%2812x%5E2%29%2F%283x%5E2%2B12x%29%29%2A%28%28x%5E2%2Bx-12%29%2F%284x%5E3-36x%29%29 Multiply the 1st fraction by the reciprocal of the 2nd


%28%2812x%5E2%29%2F%283x%5E2%2B12x%29%29%2A%28%28x%5E2%2Bx-12%29%2F%28x%284x%5E2-36%29%29%29 Factor out an x from the denominator of the right term

Factor out an x from the denominator of the left term

Factor the numerator of the 1st term x%5E2%2Bx-12

Solved by pluggable solver: Factoring Quadratics with a leading coefficient of 1 (a=1)
In order to factor 1%2Ax%5E2%2B1%2Ax%2B-12, first we need to ask ourselves: What two numbers multiply to -12 and add to 1? Lets find out by listing all of the possible factors of -12


Factors:

1,2,3,4,6,12,28,56,

-1,-2,-3,-4,-6,-12,-28,-56,List the negative factors as well. This will allow us to find all possible combinations

These factors pair up to multiply to -12.

(-1)*(56)=-12

(-2)*(28)=-12

(-3)*(12)=-12

(-4)*(6)=-12

Now which of these pairs add to 1? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 1

||||||||
First Number|Second Number|Sum
1|-56|1+(-56)=-55
2|-28|2+(-28)=-26
3|-12|3+(-12)=-9
4|-6|4+(-6)=-2
-1|56|(-1)+56=55
-2|28|(-2)+28=26
-3|12|(-3)+12=9
-4|6|(-4)+6=2
None of these factors add to 1. So this quadratic cannot be factored. In order to solve for x, we need to use the quadratic formula.



Now factor the denominator of the 2nd term 4x%5E2-36

ERROR Algebra::Solver::Engine::invoke_solver_noengine: solver not defined for name 'quadratic_factoring'.
Error occurred executing solver 'quadratic_factoring' .




Basically factors to:




Factor out a 2 out of 2x-6

Notice these terms cancel

Factor a 3 out of 3x%2B12

Notice these terms cancel

So we get after reducing:

%28%2812x%5E2%29%2F%283x%29%29%2A%281%2F%282x%282x%2B6%29%29%29

%28%2812x%5E2%29%2F%286x%5E2%29%282x%2B6%29%29 Now multiply

2%2F%282x%2B6%29 Divide and simplify

2%2F%282%28x%2B3%29%29 Factor out a 2

1%2F%28x%2B3%29 Divide and simplify again. This is your simplified answer.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
(12x^2)/(3x^2+12x) divided by (4x^3-36x)/(x^2+x-12)
Factor where you can:
(12x^2)/(3x(x+4) / 4x(x+3)(x-3) / (x+4)(x-3)
Cancel where you can to get: invert the denominator and multiply
(4x)/(x+4) * (x+4)/4x(x+3)
Cancel where you can to get:
= 1/(x+3)
===========
Cheers,
Stan H.