What is 9/(20m^4+100m^3)-(2m^2)/(3m^2+16m+5) ?

The solution to 9/(20m^4+100m^3)-(2m^2)/(3m^2+16m+5) is (27m+9-40m^5)/(20m^3(m+5)(3m+1))

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simplify 9/(20m^4+100m^3)-(2m^2)/(3m^2+16m+5)

simplify

\frac{9}{20 m ^{4} + 100 m ^{3}} - \frac{2 m ^{2}}{3 m ^{2} + 16 m + 5}

\frac{27 m + 9 - 40 m ^{5}}{20 m ^{3} ( m + 5 ) ( 3 m + 1 )}

Solution steps

\frac{9}{20 m ^{4} + 100 m ^{3}} - \frac{2 m ^{2}}{3 m ^{2} + 16 m + 5}

Least Common Multiplier of

20 m^{4} + 100 m^{3}, 3 m^{2} + 16 m + 5 : 20 m^{3} (m + 5) (3 m + 1)

Adjust Fractions based on the LCM

= \frac{9 ( 3 m + 1 )}{20 m ^{3} ( m + 5 ) ( 3 m + 1 )} - \frac{40 m ^{5}}{20 m ^{3} ( m + 5 ) ( 3 m + 1 )}

Apply the fraction rule:

\frac{a}{c} - \frac{b}{c} = \frac{a - b}{c}

= \frac{9 ( 3 m + 1 ) - 40 m ^{5}}{20 m ^{3} ( m + 5 ) ( 3 m + 1 )}

Simplify

9 (3 m + 1) - 40 m^{5} : 27 m + 9 - 40 m^{5}

= \frac{27 m + 9 - 40 m ^{5}}{20 m ^{3} ( m + 5 ) ( 3 m + 1 )}

- 8 < x - 7 < 8

\frac{5}{x} > 4

8 + 12 a^{2} + 6 a^{4} + a^{6}

3 s^{2} - 14 s + 8

t^{- \frac{1}{3}}

What is 9/(20m^4+100m^3)-(2m^2)/(3m^2+16m+5) ?
The solution to 9/(20m^4+100m^3)-(2m^2)/(3m^2+16m+5) is (27m+9-40m^5)/(20m^3(m+5)(3m+1))