What is the answer to (x+m)/m-(x+n)/n =(m^2+n^2)/(mn)-2 ?

The answer to (x+m)/m-(x+n)/n =(m^2+n^2)/(mn)-2 is x=n-m;\quad mn\ne 0,m\ne n

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(x+m)/m-(x+n)/n =(m^2+n^2)/(mn)-2

\frac{x + m}{m} - \frac{x + n}{n} = \frac{m ^{2} + n ^{2}}{mn} - 2

x = n - m; mn \neq = 0, m \neq = n

Solution steps

\frac{x + m}{m} - \frac{x + n}{n} = \frac{m ^{2} + n ^{2}}{mn} - 2

Multiply by LCM

n (x + m) - m (x + n) = m^{2} + n^{2} - 2 mn; mn \neq = 0

Expand

n (x + m) - m (x + n) : - m x + n x

- m x + n x = m^{2} + n^{2} - 2 mn; mn \neq = 0

Factor

- m x + n x : x (- m + n)

x (- m + n) = m^{2} + n^{2} - 2 mn; mn \neq = 0

Divide both sides by

- m + n; mn \neq = 0, m \neq = n

x = n - m; mn \neq = 0, m \neq = n

\frac{x - 9}{9} = \frac{x + 5}{7}

a, a + b = 2

- 8 = \frac{y}{9}

3 x - 4 = - 10

x, 2 y = 4 x + 10

What is the answer to (x+m)/m-(x+n)/n =(m^2+n^2)/(mn)-2 ?
The answer to (x+m)/m-(x+n)/n =(m^2+n^2)/(mn)-2 is x=n-m;\quad mn\ne 0,m\ne n