Simplify the rational expression state any restrictions on the variable t² - 4t - 32/t - 8

Solution:

The numerator of the given expression t² - 4t - 32/t - 8 is a quadratic equation of the form:

ax² + bx + c

Factorizing t² - 4t - 32 we have

t² - 8t + 4t - 32

t(t - 8) + 4(t - 8)

(t - 8)(t + 4)

Therefore

t² - 4t - 32/t - 8 = [(t - 8)(t + 4)]/(t - 8)]

The above equation can be simplified with an assumption/restriction which is :

t ≠ 8

[(t - 8)(t + 4)]/(t - 8)] = (t + 4)

Simplify the rational expression state any restrictions on the variable t² - 4t - 32/t - 8

Summary:

Simplifying t² - 4t - 32/t - 8 we have (t + 4) with the restriction t ≠ 8