SOLUTION: Divide. x^2+2x-15/4x^2 / x^2-25/2x-10 Thank you.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Divide. x^2+2x-15/4x^2 / x^2-25/2x-10 Thank you.      Log On


   

Question 29746: Divide. x^2+2x-15/4x^2 / x^2-25/2x-10
Thank you.
Found 2 solutions by Cintchr, sdmmadam@yahoo.com:
Answer by Cintchr(481) About Me  (Show Source):
You can put this solution on YOUR website!
+%28%28x%5E2%2B2x-15%29%2F%284x%5E2%29%29+%2F+%28%28x%5E2-25%29%2F%282x-10%29%29+
factor all parts

looking at each fraction separately .... reduce the fractions
+%28%28x%2B5%29%28x-3%29%2F%284x%5E2%29%29+%2F+%28%28%28x%2B5%29%29%2F2%29+
multiple outides / multiply insides
+%282%28x%2B5%29%28x-3%29%29+%2F+%28%284x%5E2%29%28x%2B5%29%29+
reduce
+%282%28x-3%29%29+%2F+%284x%5E2%29+
reduce again
+%28%28x-3%29%29+%2F+%282x%5E2%29+

Answer by sdmmadam@yahoo.com(530) About Me  (Show Source):
You can put this solution on YOUR website!
Divide. x^2+2x-15/4x^2 / x^2-25/2x-10
Thank you.
[(x^2+2x-15)/(4x^2)] / [(x^2-25)/(2x-10)]
= [(x+5)(x-3)/ (4x^2)] / [(x+5)(x-5)/2(x-5)]
(factorising the nr in the first fraction
and using formula a^2-b^2 = (a+b)(a-b) and here a = x and b = 5)
= [(x+5)(x-3)/ (4x^2)] divided by [(x+5)/2]
(canceling (x-5) in the nr and in the dr in the second fraction)
= [(x+5)(x-3)/ (4x^2)] multiplied by [2/(x+5)] (when division symbol is replaced by multiplication symbol then the fraction
that is after the division symbol is reciprocated)
= [(x+5)(x-3)/ (4x^2)]X [2/(x+5)]
= [2(x+5)(x-3)/ (4x^2)(x+5)]
= [(x-3)/ (2x^2)] (canceling (x+5) )
= (x-3)/ 2x^2