Algebra Examples

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

Step 1

Cancel the common factor of $1$ .

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Step 1.1

Cancel the common factor.

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

Step 1.2

Rewrite the expression.

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

Step 2

Multiply the numerator and denominator of the fraction by $t$ .

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Step 2.1

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

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

Step 2.2

Combine.

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

Step 3

Apply the distributive property.

$\frac{t \frac{1}{t} + t (- 1 \cdot 1)}{t \cdot t + t \cdot - 1}$

Step 4

Cancel the common factor of $t$ .

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Step 4.1

Cancel the common factor.

$\frac{t \frac{1}{t} + t (- 1 \cdot 1)}{t \cdot t + t \cdot - 1}$

Step 4.2

Rewrite the expression.

$\frac{1 + t (- 1 \cdot 1)}{t \cdot t + t \cdot - 1}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $- 1$ by $1$ .

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

Step 5.2

Move $- 1$ to the left of $t$ .

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

Step 5.3

Rewrite $- 1 t$ as $- t$ .

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

Step 6

Simplify the denominator.

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Step 6.1

Multiply $t$ by $t$ .

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

Step 6.2

Move $- 1$ to the left of $t$ .

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

Step 6.3

Rewrite $- 1 t$ as $- t$ .

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

Step 6.4

Factor $t$ out of $t^{2} - t$ .

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Step 6.4.1

Factor $t$ out of $t^{2}$ .

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

Step 6.4.2

Factor $t$ out of $- t$ .

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

Step 6.4.3

Factor $t$ out of $t \cdot t + t \cdot - 1$ .

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

Step 7

Reduce the expression by cancelling the common factors.

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Step 7.1

Cancel the common factor of $1 - t$ and $t - 1$ .

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Step 7.1.1

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

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

Step 7.1.2

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

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

Step 7.1.3

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

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

Step 7.1.4

Reorder terms.

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

Step 7.1.5

Cancel the common factor.

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

Step 7.1.6

Rewrite the expression.

$\frac{- 1}{t}$

Step 7.2

Move the negative in front of the fraction.

$- \frac{1}{t}$