# Divide ((m+6)/(m-4))÷((m+4)/(m^2-5m+4))

m+6m-4÷m+4m2-5m+4
To divide by a fraction, multiply by its reciprocal.
m+6m-4⋅m2-5m+4m+4
Factor m2-5m+4 using the AC method.
Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is 4 and whose sum is -5.
-4,-1
Write the factored form using these integers.
m+6m-4⋅(m-4)(m-1)m+4
m+6m-4⋅(m-4)(m-1)m+4
Cancel the common factor of m-4.
Cancel the common factor.
m+6m-4⋅(m-4)(m-1)m+4
Rewrite the expression.
(m+6)m-1m+4
(m+6)m-1m+4
Multiply m+6 and m-1m+4.
(m+6)(m-1)m+4
Divide ((m+6)/(m-4))÷((m+4)/(m^2-5m+4))