Simplify (12m^3y^4+12m^2y^3+3my^2)/(6m^2y^2)

Math
12m3y4+12m2y3+3my26m2y2
Simplify the numerator.
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Factor 3my2 out of 12m3y4+12m2y3+3my2.
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Factor 3my2 out of 12m3y4.
3my2(4m2y2)+12m2y3+3my26m2y2
Factor 3my2 out of 12m2y3.
3my2(4m2y2)+3my2(4my)+3my26m2y2
Factor 3my2 out of 3my2.
3my2(4m2y2)+3my2(4my)+3my2(1)6m2y2
Factor 3my2 out of 3my2(4m2y2)+3my2(4my).
3my2(4m2y2+4my)+3my2(1)6m2y2
Factor 3my2 out of 3my2(4m2y2+4my)+3my2(1).
3my2(4m2y2+4my+1)6m2y2
3my2(4m2y2+4my+1)6m2y2
Rewrite m2y2 as (my)2.
3my2(4(my)2+4(my)+1)6m2y2
Let u=my. Substitute u for all occurrences of my.
3my2(4u2+4u+1)6m2y2
Factor using the perfect square rule.
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Rewrite 4u2 as (2u)2.
3my2((2u)2+4u+1)6m2y2
Rewrite 1 as 12.
3my2((2u)2+4u+12)6m2y2
Check the middle term by multiplying 2ab and compare this result with the middle term in the original expression.
2ab=2⋅(2u)⋅1
Simplify.
2ab=4u
Factor using the perfect square trinomial rule a2+2ab+b2=(a+b)2, where a=2u and b=1.
3my2(2u+1)26m2y2
3my2(2u+1)26m2y2
Replace all occurrences of u with my.
3my2(2my+1)26m2y2
3my2(2my+1)26m2y2
Reduce the expression by cancelling the common factors.
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Cancel the common factor of 3 and 6.
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Factor 3 out of 3my2(2my+1)2.
3(my2(2my+1)2)6m2y2
Cancel the common factors.
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Factor 3 out of 6m2y2.
3(my2(2my+1)2)3(2m2y2)
Cancel the common factor.
3(my2(2my+1)2)3(2m2y2)
Rewrite the expression.
my2(2my+1)22m2y2
my2(2my+1)22m2y2
my2(2my+1)22m2y2
Cancel the common factor of m and m2.
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Factor m out of my2(2my+1)2.
m(y2(2my+1)2)2m2y2
Cancel the common factors.
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Factor m out of 2m2y2.
m(y2(2my+1)2)m(2my2)
Cancel the common factor.
m(y2(2my+1)2)m(2my2)
Rewrite the expression.
y2(2my+1)22my2
y2(2my+1)22my2
y2(2my+1)22my2
Cancel the common factor of y2.
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Cancel the common factor.
y2(2my+1)22my2
Rewrite the expression.
(2my+1)22m
(2my+1)22m
(2my+1)22m
Simplify (12m^3y^4+12m^2y^3+3my^2)/(6m^2y^2)

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