Carry out the indicated operation and dropped down the answer to lowest terms.

 (x² - 5x -14/ x²-3x+2) .   (x² - 4)/x²-14x+49)

Solution

This is a multiplication.  The first thing that we have to always do in the multiplication is to factor everything into sight as much as possible.

 (x² - 5x -14/ x²-3x+2) .   (x² - 4)/x²-14x+49)=((x-7)(x+2)/(x-2)(x-1)).((x-2)(x+2)/(x-7)²)

Now, recall that we can cancel out things across a multiplication like this.

Note that it only works for multiplication and NOT for division!

In this case we do have multiplication hence cancel as much as we can and then do the multiplication to acquire the answer.

 (x² - 5x -14/ x²-3x+2) .   (x² - 4)/x²-14x+49)= (x+2) /( (x-1). (x+2) (x-7) = (x+2)² /(x-1). (x-7)