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受欢迎的代数 >

x+1/x =3 11/14

解答

x + \frac{1}{x} = 3 \frac{11}{14}

解答

x = 3 \frac{1}{2}, x = \frac{2}{7}

+1

十进制

x = 3.5, x = 0.28571 \dots

求解步骤

x + \frac{1}{x} = 3 \frac{11}{14}

将带分数转换为假分式:

3 \frac{11}{14} = \frac{53}{14}

x + \frac{1}{x} = \frac{53}{14}

乘以最小公倍数

14 x^{2} + 14 = 53 x

解

14 x^{2} + 14 = 53 x : x = \frac{7}{2}, x = \frac{2}{7}

x = \frac{7}{2}, x = \frac{2}{7}

验证解

找到无定义的点（奇点）:

x = 0

将不在定义域的点与解相综合:

x = \frac{7}{2}, x = \frac{2}{7}

将假分式转换为带分数:

\frac{7}{2} = 3 \frac{1}{2}

x = 3 \frac{1}{2}, x = \frac{2}{7}

作图

流行的例子

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

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

\frac{1}{x} + x = 2

\frac{1}{x} + x = 5

\frac{3}{x} = x

solvefor x,y= x/(x+2)

so l v e f or x, y = \frac{x}{x + 2}