Question 634705
I'm assuming that the expression is:
{{{((16a+8)/(5a^2+5))*((2a^2+a-1)/(4a^2-1))}}}
and not
{{{((16a+8)/((5a^2+5)*(2a^2+a-1)))/(4a^2-1)}}}
and not
{{{(16a+8)/((5a^2+5)*(2a^2+a-1)/(4a^2-1))}}}
You did well to put the numerators and the denominators in parentheses. It would help to put the whole fractions in parentheses, too:
((16a+8)/(5a^2+5))*((2a^2+a-1)/(4a^2-1))<br>
Back in the "good old days", when numerators and denominators were simple whole numbers, you should have learned that when you are multiplying fractions...<ul><li>It was OK to cancel factors <i>before</i> you multiplied. </li><li>Cross-canceling, canceling a factor in one fraction's numerator with the same factor in another fraction's denominator, was OK, too.</li><li>In fact, not only was it OK but it was a <i>very good idea</i> to cancel as much as possible before you multiplied. It made the rest of the problem much easier.</li></ul>For example:
{{{(12/55)*(11/40)*(2/3)*(5/16)}}}
Factoring we get:
{{{((3*4)/(5*11))*(11/(4*10))*(2/3)*(5/(4*2*2))}}}
Canceling:
{{{((cross(3)*cross(4))/(cross(5)*cross(11)))*(cross(11)/(cross(4)*10))*(cross(2)/cross(3))*(cross(5)/(cross(4)*cross(2)*2))}}}
leaving:
{{{(1/1)*(1/10)*(1/1)*(1/2)}}}
which, you must agree, will be much eaier to multiply than what we started with. Plus, we've already done all the canceling. We will not have to reduce the answer we get.<br>
The reason I went through all that was to make this point: With fractions like we have in this problem:
{{{((16a+8)/(5a^2+5))*((2a^2+a-1)/(4a^2-1))}}}
is <i><b>more important and more useful than ever before</b></i> that we try to cancel before we go ahead and multiply. So we start with factoring so we can see what will cancel, if anything:
{{{((8(2a+1))/(5(a^2+1)))*((2a-1)(a+1))/((2a+1)(2a-1)))}}}
And we do indeed get some factors we can cancel:
{{{((8cross((2a+1)))/(5(a^2+1)))*((cross((2a-1))(a+1))/(cross((2a+1))cross((2a-1)))))}}}
leaving
{{{(8/(5(a^2+1)))*((a+1)/1)}}}
This is clearly easier to multiply than what we started with. Multiplying this out we get:
{{{(8a+8)/(5a^2+5)}}}