簡約 3/(p+1)+4/(2p-6)-(p^2-5)/(p^2-2p-3)

解

簡約

\frac{3}{p + 1} + \frac{4}{2 p - 6} - \frac{p ^{2} - 5}{p ^{2} - 2 p - 3}

\frac{- p ^{2} + 5 p - 2}{( p + 1 ) ( p - 3 )}

解答ステップ

\frac{3}{p + 1} + \frac{4}{2 p - 6} - \frac{p ^{2} - 5}{p ^{2} - 2 p - 3}

キャンセル

\frac{4}{2 p - 6} : \frac{2}{p - 3}

= \frac{3}{p + 1} + \frac{2}{p - 3} - \frac{p ^{2} - 5}{p ^{2} - 2 p - 3}

簡素化

\frac{3}{p + 1} + \frac{2}{p - 3} - \frac{p ^{2} - 5}{p ^{2} - 2 p - 3} : \frac{3 ( p - 3 ) + 2 ( p + 1 ) - ( p ^{2} - 5 )}{( p + 1 ) ( p - 3 )}

= \frac{3 ( p - 3 ) + 2 ( p + 1 ) - ( p ^{2} - 5 )}{( p + 1 ) ( p - 3 )}

簡素化

3 (p - 3) + 2 (p + 1) - (p^{2} - 5) : - p^{2} + 5 p - 2

= \frac{- p ^{2} + 5 p - 2}{( p + 1 ) ( p - 3 )}