Multiply the numerator by the reciprocal of the denominator.

For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is .

Factor out of .

Rewrite as plus

Apply the distributive property.

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

Factor out the greatest common factor (GCF) from each group.

Factor the polynomial by factoring out the greatest common factor, .

Multiply and .

Rewrite as .

Rewrite as .

Since both terms are perfect squares, factor using the difference of squares formula, where and .

Cancel the common factor.

Rewrite the expression.

Divide (9t^2-4)/((3t^2+5t+2)/(t+4))