# Simplify ((2m)/(m+2))((4m^2+5m-6)/(mn))

(2mm+2)(4m2+5m-6mn)
Factor by grouping.
For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=4⋅-6=-24 and whose sum is b=5.
Factor 5 out of 5m.
2mm+2⋅4m2+5(m)-6mn
Rewrite 5 as -3 plus 8
2mm+2⋅4m2+(-3+8)m-6mn
Apply the distributive property.
2mm+2⋅4m2-3m+8m-6mn
2mm+2⋅4m2-3m+8m-6mn
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
2mm+2⋅(4m2-3m)+8m-6mn
Factor out the greatest common factor (GCF) from each group.
2mm+2⋅m(4m-3)+2(4m-3)mn
2mm+2⋅m(4m-3)+2(4m-3)mn
Factor the polynomial by factoring out the greatest common factor, 4m-3.
2mm+2⋅(4m-3)(m+2)mn
2mm+2⋅(4m-3)(m+2)mn
Cancel the common factor of m.
Factor m out of 2m.
m⋅2m+2⋅(4m-3)(m+2)mn
Factor m out of mn.
m⋅2m+2⋅(4m-3)(m+2)m(n)
Cancel the common factor.
m⋅2m+2⋅(4m-3)(m+2)mn
Rewrite the expression.
2m+2⋅(4m-3)(m+2)n
2m+2⋅(4m-3)(m+2)n
Cancel the common factor of m+2.
Factor m+2 out of (4m-3)(m+2).
2m+2⋅(m+2)(4m-3)n
Cancel the common factor.
2m+2⋅(m+2)(4m-3)n
Rewrite the expression.
24m-3n
24m-3n
Combine 2 and 4m-3n.
2(4m-3)n
Simplify ((2m)/(m+2))((4m^2+5m-6)/(mn))

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