Solve F(y)=(1/y^2-3/y^4)(y+9y^3)

$$F ( y ) = ( \frac { 1 } { y ^ { 2 } } - \frac { 3 } { y ^ { 4 } } ) ( y + 9 y ^ { 3 } )$$

Evaluate

$$9y-\frac{26}{y}-\frac{3}{y^{3}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y^{2} and y^{4} is y^{4}. Multiply \frac{1}{y^{2}} times \frac{y^{2}}{y^{2}}.

$$\left(\frac{y^{2}}{y^{4}}-\frac{3}{y^{4}}\right)\left(y+9y^{3}\right)$$

Since \frac{y^{2}}{y^{4}} and \frac{3}{y^{4}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{y^{2}-3}{y^{4}}\left(y+9y^{3}\right)$$

Express \frac{y^{2}-3}{y^{4}}\left(y+9y^{3}\right) as a single fraction.

$$\frac{\left(y^{2}-3\right)\left(y+9y^{3}\right)}{y^{4}}$$

Factor the expressions that are not already factored.

$$\frac{y\left(y^{2}-3\right)\left(9y^{2}+1\right)}{y^{4}}$$

Cancel out y in both numerator and denominator.

$$\frac{\left(y^{2}-3\right)\left(9y^{2}+1\right)}{y^{3}}$$

Expand the expression.

$$\frac{9y^{4}-26y^{2}-3}{y^{3}}$$

Expand

$$9y-\frac{26}{y}-\frac{3}{y^{3}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y^{2} and y^{4} is y^{4}. Multiply \frac{1}{y^{2}} times \frac{y^{2}}{y^{2}}.

$$\left(\frac{y^{2}}{y^{4}}-\frac{3}{y^{4}}\right)\left(y+9y^{3}\right)$$

Since \frac{y^{2}}{y^{4}} and \frac{3}{y^{4}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{y^{2}-3}{y^{4}}\left(y+9y^{3}\right)$$

Express \frac{y^{2}-3}{y^{4}}\left(y+9y^{3}\right) as a single fraction.

$$\frac{\left(y^{2}-3\right)\left(y+9y^{3}\right)}{y^{4}}$$

Factor the expressions that are not already factored.

$$\frac{y\left(y^{2}-3\right)\left(9y^{2}+1\right)}{y^{4}}$$

Cancel out y in both numerator and denominator.

$$\frac{\left(y^{2}-3\right)\left(9y^{2}+1\right)}{y^{3}}$$

Expand the expression.

$$\frac{9y^{4}-26y^{2}-3}{y^{3}}$$