Write the rational expression in simplest form and get the restrictions.
(x^2+ 3x -40) / (x^2 +12x +32)
To simplify the rational expression (x^2 + 3x - 40) / (x^2 + 12x + 32), we need to factor the numerator and the denominator and then cancel out any common factors.
Let's start by factoring the numerator:
x^2 + 3x - 40 = (x + 8)(x - 5)
Now, let's factor the denominator:
x^2 + 12x + 32 = (x + 4)(x + 8)
Now we can write the simplified form of the rational expression:
(x^2 + 3x - 40) / (x^2 + 12x + 32) = (x + 8)(x - 5) / (x + 4)(x + 8)
Notice that we can cancel out the factor (x + 8) in both the numerator and the denominator, which leaves us with:
(x - 5) / (x + 4)
The restrictions for this expression occur when the denominator becomes zero, since division by zero is undefined. In this case, the denominator (x + 4) becomes zero when x = -4. Therefore, the restriction for this rational expression is x ≠ -4.
Both top and bottom factor
Go for it !
the answer i got is (x-5)/(x+4). now how do i get the restriction?
hello, why no response
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.
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 )
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