Basic Math Examples

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

Step 1

Simplify each term.

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Step 1.1

To divide by a fraction, multiply by its reciprocal.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Multiply $2$ by $1$ .

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

Step 1.4

Apply the distributive property.

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

Step 1.5

Multiply $2$ by $- 1$ .

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

Step 1.6

Multiply $- 1$ by $2$ .

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

Step 2

Find the common denominator.

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

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

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

Step 2.4

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

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

Step 2.5

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

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

Step 2.6

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

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

Step 2.7

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

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

Step 2.8

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

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

Step 2.9

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

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

Step 3

Combine the numerators over the common denominator.

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

Step 4

Simplify each term.

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Step 4.1

Apply the distributive property.

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

Step 4.2

Multiply $t$ by $t$ by adding the exponents.

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Step 4.2.1

Move $t$ .

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

Step 4.2.2

Multiply $t$ by $t$ .

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

Step 4.3

Multiply $- 2$ by $1$ .

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

Step 4.4

Apply the distributive property.

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

Step 4.5

Multiply $- 2$ by $1$ .

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

Step 5

Simplify terms.

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Step 5.1

Subtract $2 t$ from $t$ .

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

Step 5.2

Combine the opposite terms in $- 2 t^{2} - t - 2 t - 2 + t + 1$ .

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Step 5.2.1

Add $- t$ and $t$ .

$\frac{- 2 t^{2} - 2 t - 2 + 0 + 1}{t + 1}$

Step 5.2.2

Add $- 2 t^{2} - 2 t - 2$ and $0$ .

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

Step 5.3

Add $- 2$ and $1$ .

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

Step 5.4

Factor $- 1$ out of $- 2 t^{2}$ .

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

Step 5.5

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

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

Step 5.6

Factor $- 1$ out of $- (2 t^{2}) - (2 t)$ .

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

Step 5.7

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

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

Step 5.8

Factor $- 1$ out of $- (2 t^{2} + 2 t) - 1 (1)$ .

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

Step 5.9

Simplify the expression.

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Step 5.9.1

Rewrite $- (2 t^{2} + 2 t + 1)$ as $- 1 (2 t^{2} + 2 t + 1)$ .

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

Step 5.9.2

Move the negative in front of the fraction.

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