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受欢迎的代数 >

x/(1-1/x)=x+3

解答

\frac{x}{1 - \frac{1}{x}} = x + 3

解答

x = \frac{3}{2}

+1

十进制

x = 1.5

求解步骤

\frac{x}{1 - \frac{1}{x}} = x + 3

化简

\frac{x}{1 - \frac{1}{x}} : \frac{x ^{2}}{x - 1}

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

在两边乘以

x - 1

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

乘开

x (x - 1) : x^{2} - x

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

乘开

3 (x - 1) : 3 x - 3

x^{2} = x^{2} - x + 3 x - 3

同类项相加:

- x + 3 x = 2 x

x^{2} = x^{2} + 2 x - 3

两边减去

x^{2} + 2 x

x^{2} - (x^{2} + 2 x) = x^{2} + 2 x - 3 - (x^{2} + 2 x)

化简

- 2 x = - 3

两边除以

- 2

x = \frac{3}{2}

验证解

找到无定义的点（奇点）:

x = 1, x = 0

将不在定义域的点与解相综合:

x = \frac{3}{2}

作图

流行的例子

1/(x+2)-3=(10)/(x+2)

\frac{1}{x + 2} - 3 = \frac{10}{x + 2}

\frac{45}{5 + y} = 13

solvefor x,y=(x+3)/(2x-8)

so l v e f or x, y = \frac{x + 3}{2 x - 8}

z + \frac{10}{z} - 6 = 0

α = \frac{λ}{α}