Solve (9-9/n^2)(3/n)

$$( 9 - \frac { 9 } { n ^ { 2 } } ) ( \frac { 3 } { n } )$$

Evaluate

$$\frac{27\left(n^{2}-1\right)}{n^{3}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 9 times \frac{n^{2}}{n^{2}}.

$$\left(\frac{9n^{2}}{n^{2}}-\frac{9}{n^{2}}\right)\times \frac{3}{n}$$

Since \frac{9n^{2}}{n^{2}} and \frac{9}{n^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9n^{2}-9}{n^{2}}\times \frac{3}{n}$$

Multiply \frac{9n^{2}-9}{n^{2}} times \frac{3}{n} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(9n^{2}-9\right)\times 3}{n^{2}n}$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{\left(9n^{2}-9\right)\times 3}{n^{3}}$$

Use the distributive property to multiply 9n^{2}-9 by 3.

$$\frac{27n^{2}-27}{n^{3}}$$

Expand

$$\frac{27\left(n^{2}-1\right)}{n^{3}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 9 times \frac{n^{2}}{n^{2}}.

$$\left(\frac{9n^{2}}{n^{2}}-\frac{9}{n^{2}}\right)\times \frac{3}{n}$$

Since \frac{9n^{2}}{n^{2}} and \frac{9}{n^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9n^{2}-9}{n^{2}}\times \frac{3}{n}$$

Multiply \frac{9n^{2}-9}{n^{2}} times \frac{3}{n} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(9n^{2}-9\right)\times 3}{n^{2}n}$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{\left(9n^{2}-9\right)\times 3}{n^{3}}$$

Use the distributive property to multiply 9n^{2}-9 by 3.

$$\frac{27n^{2}-27}{n^{3}}$$