Solve n+1/n+10=n/n+6

$$\frac { n + 1 } { n + 10 } = \frac { n } { n + 6 }$$

Solve for n

$$n=2$$

Steps for Solving Linear Equation

Variable n cannot be equal to any of the values -10,-6 since division by zero is not defined. Multiply both sides of the equation by \left(n+6\right)\left(n+10\right), the least common multiple of n+10,n+6.

$$\left(n+6\right)\left(n+1\right)=\left(n+10\right)n$$

Use the distributive property to multiply n+6 by n+1 and combine like terms.

$$n^{2}+7n+6=\left(n+10\right)n$$

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

$$n^{2}+7n+6=n^{2}+10n$$

Subtract n^{2} from both sides.

$$n^{2}+7n+6-n^{2}=10n$$

Combine n^{2} and -n^{2} to get 0.

$$7n+6=10n$$

Subtract 10n from both sides.

$$7n+6-10n=0$$

Combine 7n and -10n to get -3n.

$$-3n+6=0$$

Subtract 6 from both sides. Anything subtracted from zero gives its negation.

$$-3n=-6$$

Divide both sides by -3.

$$n=\frac{-6}{-3}$$

Divide -6 by -3 to get 2.

$$n=2$$