quotient and simplify

Question

Find the quotient and simplify x+7/6-x divide by x²-4x-21/x²-13x+42

Answer 1

Hi Caroline,

 

(x+7)/(6-x) ÷ (x² - 4x -21)/(x² -13x + 42)

 

= (x+7)/(6-x) • (x² -13x + 42)/(x² - 4x -21) where the division problem becomes a multiplication problem where we invert the second rational expression.

 

Now we factor.

 

= (x+7)/(6-x) • ((x - 7)(x - 6))/((x-7)(x+3))

 

Let's pull a -1 out of the (6 - x) factor to create -(x - 6).

 

= -(x+7)/(x-6) • ((x - 7)(x - 6))/((x-7)(x+3))

 

We can now cancel out the factors (x - 6) and (x - 7) which leaves

 

= -(x+7)/(x+3)