Solve 840/m+10+2=840/n

$$\frac { 840 } { m + 10 } + 2 = \frac { 840 } { n }$$

Solve for m

$$m=-\frac{10\left(43n-420\right)}{n-420}$$

$$n\neq 0\text{ and }n\neq 420$$

Steps for Solving Linear Equation

Variable m cannot be equal to -10 since division by zero is not defined. Multiply both sides of the equation by n\left(m+10\right), the least common multiple of m+10,n.

$$n\times 840+n\left(m+10\right)\times 2=\left(m+10\right)\times 840$$

Use the distributive property to multiply n by m+10.

$$n\times 840+\left(nm+10n\right)\times 2=\left(m+10\right)\times 840$$

Use the distributive property to multiply nm+10n by 2.

$$n\times 840+2nm+20n=\left(m+10\right)\times 840$$

Combine n\times 840 and 20n to get 860n.

$$860n+2nm=\left(m+10\right)\times 840$$

Use the distributive property to multiply m+10 by 840.

$$860n+2nm=840m+8400$$

Subtract 840m from both sides.

$$860n+2nm-840m=8400$$

Subtract 860n from both sides.

$$2nm-840m=8400-860n$$

Combine all terms containing m.

$$\left(2n-840\right)m=8400-860n$$

Divide both sides by 2n-840.

$$\frac{\left(2n-840\right)m}{2n-840}=\frac{8400-860n}{2n-840}$$

Dividing by 2n-840 undoes the multiplication by 2n-840.

$$m=\frac{8400-860n}{2n-840}$$

Divide 8400-860n by 2n-840.

$$m=\frac{10\left(420-43n\right)}{n-420}$$

Variable m cannot be equal to -10.

$$m=\frac{10\left(420-43n\right)}{n-420}\text{, }m\neq -10$$

Solve for n

$$n=\frac{420\left(m+10\right)}{m+430}$$

$$m\neq -10\text{ and }m\neq -430$$

Steps for Solving Linear Equation

Variable n cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by n\left(m+10\right), the least common multiple of m+10,n.

$$n\times 840+n\left(m+10\right)\times 2=\left(m+10\right)\times 840$$

Use the distributive property to multiply n by m+10.

$$n\times 840+\left(nm+10n\right)\times 2=\left(m+10\right)\times 840$$

Use the distributive property to multiply nm+10n by 2.

$$n\times 840+2nm+20n=\left(m+10\right)\times 840$$

Combine n\times 840 and 20n to get 860n.

$$860n+2nm=\left(m+10\right)\times 840$$

Use the distributive property to multiply m+10 by 840.

$$860n+2nm=840m+8400$$

Combine all terms containing n.

$$\left(860+2m\right)n=840m+8400$$

The equation is in standard form.

$$\left(2m+860\right)n=840m+8400$$

Divide both sides by 860+2m.

$$\frac{\left(2m+860\right)n}{2m+860}=\frac{840m+8400}{2m+860}$$

Dividing by 860+2m undoes the multiplication by 860+2m.

$$n=\frac{840m+8400}{2m+860}$$

Divide 8400+840m by 860+2m.

$$n=\frac{420\left(m+10\right)}{m+430}$$

Variable n cannot be equal to 0.

$$n=\frac{420\left(m+10\right)}{m+430}\text{, }n\neq 0$$