Question 230540
To simplify/reduce <i>any</i> fraction, cancel common factors. And to do this we have to have factors. So we start by factoring:
{{{(3x^2-75)/(4x^2-17x-15)}}}
{{{(3(x^2-25))/((4x + 3)(x-5))}}}
{{{(3(x+5)(x-5))/((4x + 3)(x-5))}}}
Now that it's factored, we can see that there is a common factor, (x-5), which we can cancel:
{{{(3(x+5)cross((x-5)))/((4x + 3)cross((x-5)))}}}
leaving:
{{{(3(x+5))/(4x + 3)}}}
Nothing else cancels. (Note: The 3's do <i>not</i> cancel. The one on top is a factor but the one one the bottom is not.)
All that is left is to multiply out the numerator:
{{{(3x+15)/(4x + 3)}}}