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受欢迎的代数 >

x/(x+2)+6/(x+4)=1

解答

\frac{x}{x + 2} + \frac{6}{x + 4} = 1

解答

x = - 1

求解步骤

\frac{x}{x + 2} + \frac{6}{x + 4} = 1

乘以最小公倍数

x (x + 4) + 6 (x + 2) = (x + 2) (x + 4)

乘开

x (x + 4) : x^{2} + 4 x

x^{2} + 4 x + 6 (x + 2) = (x + 2) (x + 4)

乘开

6 (x + 2) : 6 x + 12

x^{2} + 4 x + 6 x + 12 = (x + 2) (x + 4)

同类项相加:

4 x + 6 x = 10 x

x^{2} + 10 x + 12 = (x + 2) (x + 4)

展开

(x + 2) (x + 4) : x^{2} + 6 x + 8

x^{2} + 10 x + 12 = x^{2} + 6 x + 8

将

12

到右边

x^{2} + 10 x = x^{2} + 6 x - 4

两边减去

x^{2} + 6 x

x^{2} + 10 x - (x^{2} + 6 x) = x^{2} + 6 x - 4 - (x^{2} + 6 x)

化简

4 x = - 4

两边除以

4

x = - 1

验证解

找到无定义的点（奇点）:

x = - 2, x = - 4

将不在定义域的点与解相综合:

x = - 1

作图

流行的例子

(6x-1)/(x^2+7)=1

\frac{6 x - 1}{x ^{2} + 7} = 1

1 + \frac{9}{x ^{2}} = 0

0=-1+(900)/((p+10)^2)

0 = - 1 + \frac{900}{( p + 10 ) ^{2}}

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

solvefor y, 2/x+3/y =4

so l v e f or y, \frac{2}{x} + \frac{3}{y} = 4