簡約 (a-2)/(a^2-3a+4)-(a-1)/(a^2-a-2)

解

簡約

\frac{a - 2}{a ^{2} - 3 a + 4} - \frac{a - 1}{a ^{2} - a - 2}

\frac{a ^{2} - 7 a + 8}{( a + 1 ) ( a - 2 ) ( a ^{2} - 3 a + 4 )}

解答ステップ

\frac{a - 2}{a ^{2} - 3 a + 4} - \frac{a - 1}{a ^{2} - a - 2}

以下の最小公倍数:

a^{2} - 3 a + 4, a^{2} - a - 2 : (a + 1) (a - 2) (a^{2} - 3 a + 4)

LCMに基づいて分数を調整する

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

分数の規則を適用する:

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

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

簡素化

(a + 1) (a - 2)^{2} - (a - 1) (a^{2} - 3 a + 4) : a^{2} - 7 a + 8

= \frac{a ^{2} - 7 a + 8}{( a + 1 ) ( a - 2 ) ( a ^{2} - 3 a + 4 )}