Question

Write the rational expression in simplest form and get the restrictions.
(x^2+ 3x -40) / (x^2 +12x +32)

Answer 1

Both top and bottom factor
Go for it !

Answer 2

the answer i got is (x-5)/(x+4). now how do i get the restriction?

Answer 3

hello, why no response

Answer 4

Patience
Most of the tutors are volunteers and we don't sit on the computer all the time waiting for posts. I go on here when I feel like it, soo ....

you must have divided by x+8.
If x = -8, that would be zero, so you have to restrict your answer to
(x-5)/(x+4) , x ≠ -8

some authors would insist on
(x-5)/(x+4) , x ≠ -8, -4

but for x=-4, the original would be just as undefined as the final answer, so that restriction could be omitted.
whereas for x = -8, the original comes out to 0/0, while the final answer would be -3/4 , so they would not be equal for that value. Thus the restriction.
Check with your teacher if he/she requires both implicit and explicit restrictions.

Answer 5

x² +12 x + 32 = 0

The solutions of this equation are:

x = - 8 and x = - 4

If the denominator of a fraction is zero, the expression is not
a legal fraction because it's overall value is undefined.

Restrictions:

x ≠ - 8 , x ≠ - 4

By the way your result is correct.

( x² + 3 x - 40 ) / ( x² +12 x + 32 ) = ( x - 5 ) / ( x + 4 )

Answer 6

Reiny is right.

Go on:
wolframalpha. c o m

When page be open in rectangle type:

plot ( x^2 + 3 x - 40 ) / ( x^2 +12 x + 32 ) , x = - 10 to 10

and clic option =

You will see graph

For x = - 8

( x² + 3 x - 40 ) / ( x² +12 x + 32 ) is defined