Respuesta :

frika

1. Factor the expression [tex]t^2-4t-32:[/tex]

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

2. Since [tex]t-8[/tex] is placed in the denominator of the given expression, then [tex]t\neq 8.[/tex]

3. Now the expression can be simplified:

[tex]\dfrac{t^2-4t-32}{t-8}=\dfrac{(t-8)(t+4)}{t-8}=t+4.[/tex]

alinakincsem

Answer:

The simplest form of  [tex]\frac{t^2-4t-32}{t-8}[/tex] is t+4.

Step-by-step explanation:

We are given an expression [tex]\frac{t^2-4t-32}{t-8}[/tex].

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

[tex]\frac{t^2-4t-32}{t-8}[/tex]

[tex]=\frac{t^2-8t+4t-32}{t-8}[/tex]

[tex]= \frac{t(t-8)+4(t-8)}{t-8}[/tex]

[tex]=\frac{(t+4)(t-8)}{t-8}[/tex]

[tex]= t+4[/tex]

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

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