Question

simplify the rational expression. state any restrictions on the variable. t^2+3t-28/t^2-16

Answer 1

hello :
 t²-16 = t²-4² = (t-4)(t+4)
 t²+3t-28 = (t-4)(t+7)
( t²+3t-28)/( t²-16) = (t-4)(t+7)/(t-4)(t+4)
                             = (t+7)/(t+4)....( Simplify by : (t-4)) and t no 4 .

Answer 2

The point of restriction is the point where t = -4

How to solve rational expressions

Given the rational expression;

$f(t) = \frac{t^2+3t-8}{t^-16}$

Factorize the numerator and denominator to have:

$f(t) = \frac{t^2+3t-28}{t^2-16}\\f(t) = \frac{t^2+7t-4t-28}{(t+4)(t-4)}\\f(t) = \frac{t(t+7)-4(t+7)}{(t+4)(t-4)}\\f(t) = \frac{t+7}{t+4}$

The function is restricted at the point where the denominator is zero. Hence;

t + 4 = 0
t = -4

The point of restriction is the point where t = -4

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