Question 203293
Simplify:
{{{((x^2-8x+15)/(x^2+2x-35))/((-x^2-2x+15)/(x^2+9x+14))}}}
To divide fractions, you invert the second fraction and multiply.
{{{((x^2-8x+15)/(x^2+2x-35))*((x^2+9x+14)/(-x^2-2x+15))}}} Now factor each of the trinomials.
{{{(cross((x-5))(x-3)/cross((x-5))cross((x+7)))*(cross((x+7))(x+2)/(-x+3)(x+5))}}} Cancel the common factors as indicated. You now have:
{{{((x-3)/1)*((x+2)/(-x+3)(x+5))}}} Substitute {{{(-x+3) = (-1)(x-3)}}}
{{{(cross((x-3))/1)*((x+2)/((-1)*cross((x-3))(x+5)))}}} Cancel the indicated common factors to leave you with:
{{{((x+2))/(-(x+5))}}} or {{{highlight(((x+2))/((-x-5)))}}}