To divide by a fraction, multiply by its reciprocal.

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.

Rewrite as .

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

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Cancel the common factor of and .

Reorder terms.

Cancel the common factor.

Rewrite the expression.

Multiply and .

Cancel the common factor of and .

Rewrite as .

Factor out of .

Factor out of .

Reorder terms.

Cancel the common factor.

Rewrite the expression.

Move the negative in front of the fraction.

The result can be shown in multiple forms.

Exact Form:

Decimal Form:

Reduce ((k+5)/(k^2+3k-10))÷((7k+14)/(4-k^2))