Simplify the rational expression state any restrictions on the variable t² + 4t - 12/t² - 4

Solution:

The expression t² + 4t - 12/t² - 4 comprises a denominator and a numerator.

Numerator is t² + 4t - 12

Denominator is t² - 4

Lets simplify the given expression by factorizing the numerator and denominator

Factorizing the numerator we have

= t² + 6t - 2t -12

= t(t + 6) -2(t + 6)

= (t - 2)(t + 6)

Factorizing the denominator we have

t² - 4 = (t + 2)(t - 2)

We rewrite the given expression as :

= t² + 4t - 12/t² - 4

= (t - 2)(t + 6)/(t + 2)(t - 2)

(t - 2) in the numerator and denominator cancel each other and hence we get,

t² + 4t - 12/t² - 4 = (t + 6)/(t + 2)where t ≠ -2

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Simplify the rational expression state any restrictions on the variable t² + 4t - 12/t² - 4

Summary:

Simplify the rational expression state we have (t + 6)/(t + 2) where t ≠ -2 (variable restriction).