zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的代数 >

(6x-7)/(x+7)-7/(6x)=6

解答

\frac{6 x - 7}{x + 7} - \frac{7}{6 x} = 6

解答

x = - \frac{7}{43}

+1

十进制

x = - 0.16279 \dots

求解步骤

\frac{6 x - 7}{x + 7} - \frac{7}{6 x} = 6

乘以最小公倍数

6 x (6 x - 7) - 7 (x + 7) = 36 x (x + 7)

乘开

6 x (6 x - 7) : 36 x^{2} - 42 x

36 x^{2} - 42 x - 7 (x + 7) = 36 x (x + 7)

乘开

- 7 (x + 7) : - 7 x - 49

36 x^{2} - 42 x - 7 x - 49 = 36 x (x + 7)

同类项相加:

- 42 x - 7 x = - 49 x

36 x^{2} - 49 x - 49 = 36 x (x + 7)

展开

36 x (x + 7) : 36 x^{2} + 252 x

36 x^{2} - 49 x - 49 = 36 x^{2} + 252 x

将

49

到右边

36 x^{2} - 49 x = 36 x^{2} + 252 x + 49

两边减去

36 x^{2} + 252 x

36 x^{2} - 49 x - (36 x^{2} + 252 x) = 36 x^{2} + 252 x + 49 - (36 x^{2} + 252 x)

化简

- 301 x = 49

两边除以

- 301

x = - \frac{7}{43}

验证解

找到无定义的点（奇点）:

x = - 7, x = 0

将不在定义域的点与解相综合:

x = - \frac{7}{43}

作图

流行的例子

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

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

-16/5 =(-4)/(1-r)

- \frac{16}{5} = \frac{- 4}{1 - r}

\frac{6}{x + 8} = - \frac{3}{4}

\frac{55}{x + 6} = x

\frac{11}{x + 3} = 10