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受欢迎的代数 >

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

解答

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

解答

x = - \frac{5}{2}

+1

十进制

x = - 2.5

求解步骤

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

乘以最小公倍数

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

乘开

(x + 2) (x + 3) : x^{2} + 5 x + 6

2 x^{2} + 8 x + 7 = 2 (x^{2} + 5 x + 6)

乘开

2 (x^{2} + 5 x + 6) : 2 x^{2} + 10 x + 12

2 x^{2} + 8 x + 7 = 2 x^{2} + 10 x + 12

展开

(x + 1) (x + 3) + (x + 2)^{2} : 2 x^{2} + 8 x + 7

2 x^{2} + 8 x + 7 = 2 x^{2} + 10 x + 12

将

7

到右边

2 x^{2} + 8 x = 2 x^{2} + 10 x + 5

两边减去

2 x^{2} + 10 x

2 x^{2} + 8 x - (2 x^{2} + 10 x) = 2 x^{2} + 10 x + 5 - (2 x^{2} + 10 x)

化简

- 2 x = 5

两边除以

- 2

x = - \frac{5}{2}

验证解

找到无定义的点（奇点）:

x = - 2, x = - 3

将不在定义域的点与解相综合:

x = - \frac{5}{2}

作图

流行的例子

\frac{4.2}{3 x} = 7

(2x-2)/(x^2-2x+2)=0

\frac{2 x - 2}{x ^{2} - 2 x + 2} = 0

x/4-5/(2x)= 1/(4x)

\frac{x}{4} - \frac{5}{2 x} = \frac{1}{4 x}

2 x - x^{- 2} = 0

\frac{4 x ^{2}}{40 x} = 3