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Simplify the rational expression. State any restrictions on the variable. t^2-4t-32/t-8

2 Answers

4 votes

Answer:

The simplest form of
(t^2-4t-32)/(t-8) is t+4.

Explanation:

We are given an expression
(t^2-4t-32)/(t-8).

Factorizing the numerator such that the factors when multiplied give a product of -32 and when added give a result of -4:


(t^2-4t-32)/(t-8)


=(t^2-8t+4t-32)/(t-8)


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


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


= t+4

Since the denominator is
t-8 in this expression, therefore
t\\eq 8 or it will be equal to zero which will make the overall value of the fraction undefined.

User MichaelScaria
by
7.8k points
4 votes

1. Factor the expression
t^2-4t-32:


t^2-4t-32=(t-8)(t+4).

2. Since
t-8 is placed in the denominator of the given expression, then
t\\eq 8.

3. Now the expression can be simplified:


(t^2-4t-32)/(t-8)=((t-8)(t+4))/(t-8)=t+4.

User Ryan Tse
by
8.5k points

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