Simplify (6-m)/(m^3-216)

Math
6-mm3-216
Simplify the denominator.
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Rewrite 216 as 63.
6-mm3-63
Since both terms are perfect cubes, factor using the difference of cubes formula, a3-b3=(a-b)(a2+ab+b2) where a=m and b=6.
6-m(m-6)(m2+m⋅6+62)
Simplify.
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Move 6 to the left of m.
6-m(m-6)(m2+6⋅m+62)
Raise 6 to the power of 2.
6-m(m-6)(m2+6m+36)
6-m(m-6)(m2+6m+36)
6-m(m-6)(m2+6m+36)
Reduce the expression by cancelling the common factors.
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Cancel the common factor of 6-m and m-6.
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Rewrite 6 as -1(-6).
-1(-6)-m(m-6)(m2+6m+36)
Factor -1 out of -m.
-1(-6)-(m)(m-6)(m2+6m+36)
Factor -1 out of -1(-6)-(m).
-1(-6+m)(m-6)(m2+6m+36)
Reorder terms.
-1(m-6)(m-6)(m2+6m+36)
Cancel the common factor.
-1(m-6)(m-6)(m2+6m+36)
Rewrite the expression.
-1m2+6m+36
-1m2+6m+36
Move the negative in front of the fraction.
-1m2+6m+36
-1m2+6m+36
Simplify (6-m)/(m^3-216)

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