3/((x+1/2)-x^2+3x)= 6/((2x+1))+x^2-2

解答

\frac{3}{( x + \frac{1}{2} ) - x ^{2} + 3 x} = \frac{6}{( 2 x + 1 )} + x^{2} - 2

x \approx 0.84920 \dots, x \approx - 1.94927 \dots, x \approx 4.07445 \dots

求解步骤

\frac{3}{( x + \frac{1}{2} ) - x ^{2} + 3 x} = \frac{6}{( 2 x + 1 )} + x^{2} - 2

乘以最小公倍数

6 (2 x + 1) = 6 (- 2 x^{2} + 8 x + 1) + x^{2} (2 x + 1) (- 2 x^{2} + 8 x + 1) - 2 (2 x + 1) (- 2 x^{2} + 8 x + 1)

解

6 (2 x + 1) = 6 (- 2 x^{2} + 8 x + 1) + x^{2} (2 x + 1) (- 2 x^{2} + 8 x + 1) - 2 (2 x + 1) (- 2 x^{2} + 8 x + 1) : x \approx 0.84920 \dots, x \approx - 1.94927 \dots, x \approx 4.07445 \dots

x \approx 0.84920 \dots, x \approx - 1.94927 \dots, x \approx 4.07445 \dots

验证解

找到无定义的点（奇点）:

x = - \frac{- 4 + 3 2}{2}, x = \frac{4 + 3 2}{2}, x = - \frac{1}{2}

将不在定义域的点与解相综合:

x \approx 0.84920 \dots, x \approx - 1.94927 \dots, x \approx 4.07445 \dots

so l v e f or x, f (x - 3) = \frac{( x ^{2} - 9 )}{( x + 1 )}

80 x^{- 2} = 6 x^{- 1} + 2

(\frac{1 - 1}{x})^{10} = 0.8

so l v e f or x, \frac{1}{x} + \frac{1}{y} + \frac{1}{z} = 1

\frac{( x + 1 )}{( 3 x - 1 )} = (\frac{20}{50})