Question 229925
{{{((25-p^2)/12)(6/(p-5))}}}<br>
Whenever you multiply fractions, it is a good idea to cancel common factors before actually multiplying. It makes the multiplying easier and the reducing of the fraction easier. In order to cancel common factors we have to have factors. So the first order of business is to factor all the numerators and denominators:
{{{(((5+p)(5-p))/(2*2*3))((2*3)/(p-5))}}}
The obvious factors that cancel are the 2's and 3's. But it is helpful to realize that (5-p) and (p-5) are negatives of each other. (Think about it.) So they will match if we factor out a -1 from one of them:
{{{(((5+p)(-1)(p-5))/(2*2*3))((2*3)/(p-5))}}}
Now can cancel to maximum effect:
{{{(((5+p)(-1)cross((p-5)))/(cross(2)*2*cross(3)))((cross(2)*cross(3))/(cross(p-5)))}}}
leaving:
{{{(((5+p)(-1))/2)(1/1)}}}
Simplifying we get:
{{{(-5-p)/2}}}