化简 ((3m))/((3m^2-1))-1/((2(3m+1)))

解答

化简

\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 )}

求解步骤

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

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

的最小公倍数:

2 (3 m + 1) (3 m + 1) (3 m - 1)

根据最小公倍数调整分式

= \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 )}

使用分式法则:

\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 )}

化简

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 )}

s im pl i f y (\frac{( - x ^{2} \cdot y )}{( z )})^{2}

s im pl i f y \frac{3 t ^{- 1}}{t ^{\frac{1}{6}}}

s im pl i f y - cos^{2} (x) tan^{2} (x)

e x p an d (a + 2 b)^{3} + 11

e x p an d (x - y)^{3} + z^{3}