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