Simplify (m^3-mn^2)/(mn^2+m^2n-2m^3)

Math
m3-mn2mn2+m2n-2m3
Simplify the numerator.
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Factor m out of m3-mn2.
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Factor m out of m3.
m⋅m2-mn2mn2+m2n-2m3
Factor m out of -mn2.
m⋅m2+m(-1n2)mn2+m2n-2m3
Factor m out of m⋅m2+m(-1n2).
m(m2-1n2)mn2+m2n-2m3
m(m2-1n2)mn2+m2n-2m3
Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=m and b=n.
m(m+n)(m-n)mn2+m2n-2m3
m(m+n)(m-n)mn2+m2n-2m3
Simplify the denominator.
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Factor m out of mn2+m2n-2m3.
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Factor m out of mn2.
m(m+n)(m-n)m(n2)+m2n-2m3
Factor m out of m2n.
m(m+n)(m-n)m(n2)+m(mn)-2m3
Factor m out of -2m3.
m(m+n)(m-n)m(n2)+m(mn)+m(-2m2)
Factor m out of m(n2)+m(mn).
m(m+n)(m-n)m(n2+mn)+m(-2m2)
Factor m out of m(n2+mn)+m(-2m2).
m(m+n)(m-n)m(n2+mn-2m2)
m(m+n)(m-n)m(n2+mn-2m2)
Factor by grouping.
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For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=-2⋅1=-2 and whose sum is b=1.
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Reorder terms.
m(m+n)(m-n)m(-2m2+n2+mn)
Reorder n2 and mn.
m(m+n)(m-n)m(-2m2+mn+n2)
Factor 1 out of mn.
m(m+n)(m-n)m(-2m2+1(mn)+n2)
Rewrite 1 as -1 plus 2
m(m+n)(m-n)m(-2m2+(-1+2)(mn)+n2)
Apply the distributive property.
m(m+n)(m-n)m(-2m2-1(mn)+2(mn)+n2)
Move parentheses.
m(m+n)(m-n)m(-2m2-1mn+2mn+n2)
m(m+n)(m-n)m(-2m2-1mn+2mn+n2)
Factor out the greatest common factor from each group.
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Group the first two terms and the last two terms.
m(m+n)(m-n)m((-2m2-1mn)+2mn+n2)
Factor out the greatest common factor (GCF) from each group.
m(m+n)(m-n)m(m(-2m-1n)-n(-2m-n))
m(m+n)(m-n)m(m(-2m-1n)-n(-2m-n))
Factor the polynomial by factoring out the greatest common factor, -2m-1n.
m(m+n)(m-n)m((-2m-1n)(m-n))
m(m+n)(m-n)m((-2m-1n)(m-n))
Rewrite -1n as -n.
m(m+n)(m-n)m(-2m-n)(m-n)
m(m+n)(m-n)m(-2m-n)(m-n)
Simplify terms.
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Cancel the common factor of m.
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Cancel the common factor.
m(m+n)(m-n)m(-2m-n)(m-n)
Rewrite the expression.
(m+n)(m-n)(-2m-n)(m-n)
(m+n)(m-n)(-2m-n)(m-n)
Cancel the common factor of m-n.
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Cancel the common factor.
(m+n)(m-n)(-2m-n)(m-n)
Rewrite the expression.
m+n-2m-n
m+n-2m-n
Factor -1 out of -2m.
m+n-(2m)-n
Factor -1 out of -n.
m+n-(2m)-(n)
Factor -1 out of -(2m)-(n).
m+n-(2m+n)
Rewrite negatives.
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Rewrite -(2m+n) as -1(2m+n).
m+n-1(2m+n)
Move the negative in front of the fraction.
-m+n2m+n
-m+n2m+n
-m+n2m+n
Simplify (m^3-mn^2)/(mn^2+m^2n-2m^3)

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