What is (2m^6+6m)/(3m^{14)+12m^9+9m^4} ?

The solution to (2m^6+6m)/(3m^{14)+12m^9+9m^4} is 2/(3m^3(m+1)(m^4-m^3+m^2-m+1))

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simplify (2m^6+6m)/(3m^{14)+12m^9+9m^4}

simplify

\frac{2 m ^{6} + 6 m}{3 m ^{14} + 12 m ^{9} + 9 m ^{4}}

\frac{2}{3 m ^{3} ( m + 1 ) ( m ^{4} - m ^{3} + m ^{2} - m + 1 )}

Solution steps

\frac{2 m ^{6} + 6 m}{3 m ^{14} + 12 m ^{9} + 9 m ^{4}}

Factor

2 m^{6} + 6 m : 2 m (m^{5} + 3)

= \frac{2 m ( m ^{5} + 3 )}{3 m ^{14} + 12 m ^{9} + 9 m ^{4}}

Factor

3 m^{14} + 12 m^{9} + 9 m^{4} : 3 m^{4} (m + 1) (m^{4} - m^{3} + m^{2} - m + 1) (m^{5} + 3)

= \frac{2 m ( m ^{5} + 3 )}{3 m ^{4} ( m + 1 ) ( m ^{4} - m ^{3} + m ^{2} - m + 1 ) ( m ^{5} + 3 )}

Cancel the common factor:

m^{5} + 3

= \frac{2 m}{3 m ^{4} ( m + 1 ) ( m ^{4} - m ^{3} + m ^{2} - m + 1 )}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

m^{4} = m m^{3}

= \frac{2 m}{3 m m ^{3} ( m + 1 ) ( m ^{4} - m ^{3} + m ^{2} - m + 1 )}

Cancel the common factor:

m

= \frac{2}{3 m ^{3} ( m + 1 ) ( m ^{4} - m ^{3} + m ^{2} - m + 1 )}

\frac{1}{30} \cdot 2

- 545

7 x^{2} - 2 x + 9 = 0

9 x^{2} - 30 x + 25

2 (2 a + 3) = - 3 (a - 1) + 31

What is (2m^6+6m)/(3m^{14)+12m^9+9m^4} ?
The solution to (2m^6+6m)/(3m^{14)+12m^9+9m^4} is 2/(3m^3(m+1)(m^4-m^3+m^2-m+1))