Simplify 5/t-2-3/t+1

$\frac{5}{t} - 2 - \frac{3}{t} + 1$

Combine the numerators over the common denominator.

$- 2 + 1 + \frac{5 - 3}{t}$

Subtract $3$ from $5$ .

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

Find the common denominator.

Write $- 2$ as a fraction with denominator $1$ .

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

Multiply $\frac{- 2}{1}$ by $\frac{t}{t}$ .

$\frac{- 2}{1} \cdot \frac{t}{t} + 1 + \frac{2}{t}$

Multiply $\frac{- 2}{1}$ by $\frac{t}{t}$ .

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

Write $1$ as a fraction with denominator $1$ .

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

Multiply $\frac{1}{1}$ by $\frac{t}{t}$ .

$\frac{- 2 t}{t} + \frac{1}{1} \cdot \frac{t}{t} + \frac{2}{t}$

Multiply $\frac{1}{1}$ by $\frac{t}{t}$ .

$\frac{- 2 t}{t} + \frac{t}{t} + \frac{2}{t}$

Combine the numerators over the common denominator.

$\frac{- 2 t + t + 2}{t}$

Add $- 2 t$ and $t$ .

$\frac{- t + 2}{t}$

Factor $- 1$ out of $- t$ .

$\frac{- (t) + 2}{t}$

Rewrite $2$ as $- 1 (- 2)$ .

$\frac{- (t) - 1 (- 2)}{t}$

Factor $- 1$ out of $- (t) - 1 (- 2)$ .

$\frac{- (t - 2)}{t}$

Simplify the expression.

Rewrite $- (t - 2)$ as $- 1 (t - 2)$ .

$\frac{- 1 (t - 2)}{t}$

Move the negative in front of the fraction.

$- \frac{t - 2}{t}$