What is ((3m))/((3m^2-1))-1/((2(3m+1))) ?

The solution to ((3m))/((3m^2-1))-1/((2(3m+1))) is (15m^2+6m+1)/(2(3m+1)(3m^2-1))

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simplify ((3m))/((3m^2-1))-1/((2(3m+1)))

simplify

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

\frac{15 m ^{2} + 6 m + 1}{2 ( 3 m + 1 ) ( 3 m ^{2} - 1 )}

Solution steps

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

Least Common Multiplier of

3 m^{2} - 1, 2 (3 m + 1) : 2 (3 m + 1) (3 m + 1) (3 m - 1)

Adjust Fractions based on the LCM

= \frac{6 m ( 3 m + 1 )}{2 ( 3 m + 1 ) ( 3 m + 1 ) ( 3 m - 1 )} - \frac{( 3 m + 1 ) ( 3 m - 1 )}{2 ( 3 m + 1 ) ( 3 m + 1 ) ( 3 m - 1 )}

Apply the fraction rule:

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

= \frac{6 m ( 3 m + 1 ) - ( 3 m + 1 ) ( 3 m - 1 )}{2 ( 3 m + 1 ) ( 3 m + 1 ) ( 3 m - 1 )}

Simplify

6 m (3 m + 1) - (3 m + 1) (3 m - 1) : 15 m^{2} + 6 m + 1

= \frac{15 m ^{2} + 6 m + 1}{2 ( 3 m + 1 ) ( 3 m + 1 ) ( 3 m - 1 )}

Apply Difference of Two Squares

(3 m + 1) (3 m - 1) : 3 m^{2} - 1

= \frac{15 m ^{2} + 6 m + 1}{2 ( 3 m + 1 ) ( 3 m ^{2} - 1 )}

(\frac{( - x ^{2} \cdot y )}{( z )})^{2}

\frac{3 t ^{- 1}}{t ^{\frac{1}{6}}}

- cos^{2} (x) tan^{2} (x)

(a + 2 b)^{3} + 11

(x - y)^{3} + z^{3}

What is ((3m))/((3m^2-1))-1/((2(3m+1))) ?
The solution to ((3m))/((3m^2-1))-1/((2(3m+1))) is (15m^2+6m+1)/(2(3m+1)(3m^2-1))