3/((5-x))+2/((4-x))= 8/((x+2))

解答

\frac{3}{( 5 - x )} + \frac{2}{( 4 - x )} = \frac{8}{( x + 2 )}

x = 2, x = \frac{58}{13}

十进制

x = 2, x = 4.46153 \dots

求解步骤

\frac{3}{( 5 - x )} + \frac{2}{( 4 - x )} = \frac{8}{( x + 2 )}

乘以最小公倍数

3 (- x + 4) (x + 2) + 2 (- x + 5) (x + 2) = 8 (- x + 5) (- x + 4)

解

3 (- x + 4) (x + 2) + 2 (- x + 5) (x + 2) = 8 (- x + 5) (- x + 4) : x = 2, x = \frac{58}{13}

x = 2, x = \frac{58}{13}

验证解

找到无定义的点（奇点）:

x = 4, x = 5, x = - 2

将不在定义域的点与解相综合:

x = 2, x = \frac{58}{13}

\frac{4}{∣ x + 1 ∣ - 2} = ∣ x + 1 ∣

\frac{- 5}{11} = \frac{5 b - 4}{2 b + 12}

\frac{x ^{2} + 3}{4 x} = \frac{1}{4}

6 \frac{m}{( m + 222 )} \cdot 100 = 10, m

\frac{( x - 1 )}{( x - 2 )} + \frac{( x - 2 )}{( x - 1 )} = \frac{5}{2}