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受欢迎的代数 >

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

解答

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

解答

x = \frac{2}{7}

+1

十进制

x = 0.28571 \dots

求解步骤

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

乘以最小公倍数

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

乘开

2 (3 x - 1) : 6 x - 2

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

展开

x (3 x - 1) : 3 x^{2} - x

3 x^{2} + 6 x - 2 = 3 x^{2} - x

将

2

到右边

3 x^{2} + 6 x = 3 x^{2} - x + 2

两边减去

3 x^{2} - x

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

化简

7 x = 2

两边除以

7

x = \frac{2}{7}

验证解

找到无定义的点（奇点）:

x = \frac{1}{3}, x = 0

将不在定义域的点与解相综合:

x = \frac{2}{7}

作图

流行的例子

solvefor c,p=(x-c)/(x+c)

so l v e f or c, p = \frac{x - c}{x + c}

\frac{1}{x} = - \frac{6}{3 x} + 5

(3x+2)/(x^2+7x+12)=0

\frac{3 x + 2}{x ^{2} + 7 x + 12} = 0

400y^{-4}-41y^{-2}+1=0

400 y^{- 4} - 41 y^{- 2} + 1 = 0

\frac{6}{9} = \frac{8}{x}