# Reduce ((k+5)/(k^2+3k-10))÷((7k+14)/(4-k^2)) To divide by a fraction, multiply by its reciprocal.
Factor using the AC method.
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 of .
Cancel the common factor.
Rewrite the expression.
Simplify the numerator.
Rewrite as .
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Simplify terms.
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))     