SOLUTION: Could you please help me with this problem simplify as much as possible {{{x^2-x-12 over 8x^2}}}Divided by {{{x^3+3x^2over 8x^3-2x^2}}} divided by 4x-1 over x+2

Algebra ->  Rational-functions -> SOLUTION: Could you please help me with this problem simplify as much as possible {{{x^2-x-12 over 8x^2}}}Divided by {{{x^3+3x^2over 8x^3-2x^2}}} divided by 4x-1 over x+2      Log On


   

Question 29912: Could you please help me with this problem
simplify as much as possible
x%5E2-x-12+over+8x%5E2Divided by x%5E3%2B3x%5E2over+8x%5E3-2x%5E2 divided by 4x-1 over x+2
Answer by Cintchr(481) About Me  (Show Source):
You can put this solution on YOUR website!
+%28x%5E2-x-12%29%2F%288x%5E2%29+Divided by +%28x%5E3%2B3x%5E2%29%2F%288x%5E3-2x%5E2%29+ divided by +%284x-1%29%2F%28x%2B2%29+
Great problem!!
first of all lets review PEMDAS (order of opperations) since each term is being divided we are working left to right. so looking at the first two fractions we find the reciprocal (flip) of the second one and multiply.
divided by +%284x-1%29%2F%28x%2B2%29+
since we are dividing by the 3rd fraction .. lets take its reciprocal and multiply as well.

factor the numerator of each fraction.

factor the denominators.

cross cancel the x + 3

cross cancel the 4x - 1
+%28%28x-4%29%2F%288x%5E2%29%29%2A%28%282x%5E2%29%2F%28x%5E2%29%29%2A%28%28x%2B2%29%2F1%29+
cross cancel the x^2 and reduce the 2 and 8
+%28%28x-4%29%2F%284%29%29%2A%28%281%29%2F%28x%5E2%29%29%2A%28%28x%2B2%29%2F1%29+
multiply ( I would leave the numerator factored out)
+%28%28x-4%29%28x%2B2%29%29%2F%284x%5E2%29+