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

Math
To divide by a fraction, multiply by its reciprocal.
Factor using the AC method.
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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.
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For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is .
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Factor out of .
Rewrite as plus
Apply the distributive property.
Multiply by .
Factor out the greatest common factor from each group.
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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 .
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Factor out of .
Factor out of .
Factor out of .
Factor out of .
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Factor out of .
Factor out of .
Factor out of .
Cancel the common factor of .
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Factor out of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Multiply and .
Cancel the common factor of and .
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Factor out of .
Rewrite as .
Factor out of .
Rewrite as .
Cancel the common factor.
Rewrite the expression.
Simplify the expression.
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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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