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受欢迎的代数 >

(4x)/(x+1)+2/(x-3)=4

解答

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

解答

x = 7

求解步骤

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

乘以最小公倍数

4 x (x - 3) + 2 (x + 1) = 4 (x + 1) (x - 3)

乘开

4 x (x - 3) : 4 x^{2} - 12 x

4 x^{2} - 12 x + 2 (x + 1) = 4 (x + 1) (x - 3)

乘开

2 (x + 1) : 2 x + 2

4 x^{2} - 12 x + 2 x + 2 = 4 (x + 1) (x - 3)

同类项相加:

- 12 x + 2 x = - 10 x

4 x^{2} - 10 x + 2 = 4 (x + 1) (x - 3)

乘开

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

4 x^{2} - 10 x + 2 = 4 (x^{2} - 2 x - 3)

乘开

4 (x^{2} - 2 x - 3) : 4 x^{2} - 8 x - 12

4 x^{2} - 10 x + 2 = 4 x^{2} - 8 x - 12

将

2

到右边

4 x^{2} - 10 x = 4 x^{2} - 8 x - 14

两边减去

4 x^{2} - 8 x

4 x^{2} - 10 x - (4 x^{2} - 8 x) = 4 x^{2} - 8 x - 14 - (4 x^{2} - 8 x)

化简

- 2 x = - 14

两边除以

- 2

x = 7

验证解

找到无定义的点（奇点）:

x = - 1, x = 3

将不在定义域的点与解相综合:

x = 7

作图

流行的例子

(x+5)((90)/x)=90

(x + 5) (\frac{90}{x}) = 90

\frac{5}{x} = 80

4=(2b+8)/(b+24)

4 = \frac{2 b + 8}{b + 24}

- \frac{4}{x} = - \frac{1}{x + 6}

\frac{2 x - 1}{x - 1} = 0