Solve 6t+6/t+6t^2-9/t^2

$$\frac { 6 t + 6 } { t } + \frac { 6 t ^ { 2 } - 9 } { t ^ { 2 } }$$

Evaluate

$$12+\frac{6}{t}-\frac{9}{t^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of t and t^{2} is t^{2}. Multiply \frac{6t+6}{t} times \frac{t}{t}.

$$\frac{\left(6t+6\right)t}{t^{2}}+\frac{6t^{2}-9}{t^{2}}$$

Since \frac{\left(6t+6\right)t}{t^{2}} and \frac{6t^{2}-9}{t^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\left(6t+6\right)t+6t^{2}-9}{t^{2}}$$

Do the multiplications in \left(6t+6\right)t+6t^{2}-9.

$$\frac{6t^{2}+6t+6t^{2}-9}{t^{2}}$$

Combine like terms in 6t^{2}+6t+6t^{2}-9.

$$\frac{12t^{2}+6t-9}{t^{2}}$$

Expand

$$12+\frac{6}{t}-\frac{9}{t^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of t and t^{2} is t^{2}. Multiply \frac{6t+6}{t} times \frac{t}{t}.

$$\frac{\left(6t+6\right)t}{t^{2}}+\frac{6t^{2}-9}{t^{2}}$$

Since \frac{\left(6t+6\right)t}{t^{2}} and \frac{6t^{2}-9}{t^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\left(6t+6\right)t+6t^{2}-9}{t^{2}}$$

Do the multiplications in \left(6t+6\right)t+6t^{2}-9.

$$\frac{6t^{2}+6t+6t^{2}-9}{t^{2}}$$

Combine like terms in 6t^{2}+6t+6t^{2}-9.

$$\frac{12t^{2}+6t-9}{t^{2}}$$