展开 ((3n)/(3n+1))-((3n-3)/(3n-2))

解答

展开

(\frac{3 n}{3 n + 1}) - (\frac{3 n - 3}{3 n - 2})

\frac{3}{9 n ^{2} - 3 n - 2}

求解步骤

(\frac{3 n}{3 n + 1}) - (\frac{3 n - 3}{3 n - 2})

去除括号:

(a) = a

= \frac{3 n}{3 n + 1} - \frac{3 n - 3}{3 n - 2}

3 n + 1, 3 n - 2

的最小公倍数:

(3 n + 1) (3 n - 2)

根据最小公倍数调整分式

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

因为分母相等，所以合并分式:

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

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

乘开

(3 n + 1) (3 n - 2) : 9 n^{2} - 3 n - 2

= \frac{3 n ( 3 n - 2 ) - ( 3 n - 3 ) ( 3 n + 1 )}{9 n ^{2} - 3 n - 2}

乘开

3 n (3 n - 2) - (3 n - 3) (3 n + 1) : 3

= \frac{3}{9 n ^{2} - 3 n - 2}

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