Question 29746
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