Write the rational expression in simplest form and get the restriction in smaller value and larger value.

(x^2-64) / (x^3 +x^2 - 64x - 64)

Restriction
(Smaller value) x≠
(Larger value) x≠

you should have no difficulty the top, I will get you started with the bottom

x^3 +x^2 - 64x - 64
= x^2(x + 1) - 64(x + 1)
= ....

i got 1/(x+1)

how do i the the smaller value restriction and larger value restriction

(x^2-64) / (x^3 +x^2 - 64x - 64)

= (x^2-64) / (x^2(x + 1) - 64(x + 1) )
= (x^2 - 64)/( (x+1)(x^2 - 64) )
= 1/(x+1) , x ≠ ±8

hey reiny, thanks, but is x ≠ ±8 is the smaller value restriction or the larger value restrictions

To simplify the rational expression (x^2-64) / (x^3 + x^2 - 64x - 64), we can factor the numerator and denominator.

Factor the numerator:
x^2 - 64 = (x+8)(x-8)

Factor the denominator:
x^3 + x^2 - 64x - 64 = (x+8)(x-4)(x+4)

Now, we can cancel out any common factors between the numerator and the denominator.

(x^2-64) / (x^3 + x^2 - 64x - 64) = (x+8)(x-8) / (x+8)(x-4)(x+4)

Simplifying the expression further, we can cancel out the common factor (x+8) in the numerator and denominator.

(x^2-64) / (x^3 + x^2 - 64x - 64) = (x-8) / (x-4)(x+4)

The simplified rational expression is (x-8) / (x-4)(x+4).

Regarding the restrictions, these occur when the denominator equals zero. Therefore, we need to find the values of x that make the denominator (x-4)(x+4) equal to zero.

Setting each factor equal to zero, we have:
x - 4 = 0 => x = 4
x + 4 = 0 => x = -4

Therefore, the restrictions are:
(Smaller value) x ≠ -4
(Larger value) x ≠ 4