Algebra Examples

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

Step 1

Combine the numerators over the common denominator.

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

Step 2

Subtract $3$ from $5$ .

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

Step 3

Find the common denominator.

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Step 3.1

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

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

Step 3.2

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

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

Step 3.3

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

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

Step 3.4

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

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

Step 3.5

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

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

Step 3.6

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

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Add $- 2 t$ and $t$ .

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

Step 6

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

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

Step 7

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

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

Step 8

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

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

Step 9

Simplify the expression.

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Step 9.1

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

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

Step 9.2

Move the negative in front of the fraction.

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