Solve 1/10n^2-n+7/n^2=1/5n^2

$$\frac { 1 } { 10 n ^ { 2 } } - \frac { n + 7 } { n ^ { 2 } } = \frac { 1 } { 5 n ^ { 2 } }$$

Solve for n

$$n = -\frac{71}{10} = -7\frac{1}{10} = -7.1$$

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 10n^{2}, the least common multiple of 10n^{2},n^{2},5n^{2}.

$$1-10\left(n+7\right)=2$$

Use the distributive property to multiply -10 by n+7.

$$1-10n-70=2$$

Subtract 70 from 1 to get -69.

$$-69-10n=2$$

Add 69 to both sides.

$$-10n=2+69$$

Add 2 and 69 to get 71.

$$-10n=71$$

Divide both sides by -10.

$$n=\frac{71}{-10}$$

Fraction \frac{71}{-10} can be rewritten as -\frac{71}{10} by extracting the negative sign.

$$n=-\frac{71}{10}$$