Rewrite the division as a fraction.

Multiply the numerator by the reciprocal of the denominator.

Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .

Write the factored form using these integers.

Cancel the common factor.

Rewrite the expression.

Multiply and .

Raise to the power of .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Divide ((t+3)/(t+4))÷(t^2+7t+12)