Simplify ((m^2-7m+12)/(2m^2-3m-2))÷((3m-9)/(-10m-5))

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.
Factor by grouping.
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.
Multiply by .
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, .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Cancel the common factor of .
Factor out of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Multiply and .
Cancel the common factor of and .
Factor out of .
Rewrite as .
Factor out of .
Rewrite as .
Cancel the common factor.
Rewrite the expression.
Simplify the expression.
Multiply by .
Move to the left of .
Move to the left of .
Move the negative in front of the fraction.
Simplify ((m^2-7m+12)/(2m^2-3m-2))÷((3m-9)/(-10m-5))

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