Solve 1/t^2+1/frac{5{t}-1}

$$\frac { \frac { 1 } { t ^ { 2 } } + 1 } { \frac { 5 } { t } - 1 }$$

Evaluate

$$-\frac{t^{2}+1}{t\left(t-5\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{t^{2}}{t^{2}}.

$$\frac{\frac{1}{t^{2}}+\frac{t^{2}}{t^{2}}}{\frac{5}{t}-1}$$

Since \frac{1}{t^{2}} and \frac{t^{2}}{t^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\frac{1+t^{2}}{t^{2}}}{\frac{5}{t}-1}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{t}{t}.

$$\frac{\frac{1+t^{2}}{t^{2}}}{\frac{5}{t}-\frac{t}{t}}$$

Since \frac{5}{t} and \frac{t}{t} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{1+t^{2}}{t^{2}}}{\frac{5-t}{t}}$$

Divide \frac{1+t^{2}}{t^{2}} by \frac{5-t}{t} by multiplying \frac{1+t^{2}}{t^{2}} by the reciprocal of \frac{5-t}{t}.

$$\frac{\left(1+t^{2}\right)t}{t^{2}\left(5-t\right)}$$

Cancel out t in both numerator and denominator.

$$\frac{t^{2}+1}{t\left(-t+5\right)}$$

Use the distributive property to multiply t by -t+5.

$$\frac{t^{2}+1}{-t^{2}+5t}$$

Expand

$$\frac{t^{2}+1}{t\left(5-t\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{t^{2}}{t^{2}}.

$$\frac{\frac{1}{t^{2}}+\frac{t^{2}}{t^{2}}}{\frac{5}{t}-1}$$

Since \frac{1}{t^{2}} and \frac{t^{2}}{t^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\frac{1+t^{2}}{t^{2}}}{\frac{5}{t}-1}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{t}{t}.

$$\frac{\frac{1+t^{2}}{t^{2}}}{\frac{5}{t}-\frac{t}{t}}$$

Since \frac{5}{t} and \frac{t}{t} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{1+t^{2}}{t^{2}}}{\frac{5-t}{t}}$$

Divide \frac{1+t^{2}}{t^{2}} by \frac{5-t}{t} by multiplying \frac{1+t^{2}}{t^{2}} by the reciprocal of \frac{5-t}{t}.

$$\frac{\left(1+t^{2}\right)t}{t^{2}\left(5-t\right)}$$

Cancel out t in both numerator and denominator.

$$\frac{t^{2}+1}{t\left(-t+5\right)}$$

Use the distributive property to multiply t by -t+5.

$$\frac{t^{2}+1}{-t^{2}+5t}$$