Calculus Examples

$\frac{\frac{1}{1 - 1.5} + 1}{1.5 - 2}$

Step 1

Multiply the numerator and denominator of the fraction by $1 - 1.5$ .

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Step 1.1

Multiply $\frac{\frac{1}{1 - 1.5} + 1}{1.5 - 2}$ by $\frac{1 - 1.5}{1 - 1.5}$ .

$\frac{1 - 1.5}{1 - 1.5} \cdot \frac{\frac{1}{1 - 1.5} + 1}{1.5 - 2}$

Step 1.2

Combine.

$\frac{(1 - 1.5) (\frac{1}{1 - 1.5} + 1)}{(1 - 1.5) (1.5 - 2)}$

Step 2

Apply the distributive property.

$\frac{(1 - 1.5) \frac{1}{1 - 1.5} + (1 - 1.5) \cdot 1}{(1 - 1.5) \cdot 1.5 + (1 - 1.5) \cdot - 2}$

Step 3

Subtract $1.5$ from $1$ .

$\frac{(1 - 1.5) \frac{1}{- 0.5} + (1 - 1.5) \cdot 1}{(1 - 1.5) \cdot 1.5 + (1 - 1.5) \cdot - 2}$

Step 4

Simplify the numerator.

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Step 4.1

Subtract $1.5$ from $1$ .

$\frac{- 0.5 (\frac{1}{- 0.5}) + (1 - 1.5) \cdot 1}{(1 - 1.5) \cdot 1.5 + (1 - 1.5) \cdot - 2}$

Step 4.2

Cancel the common factor of $0.5$ .

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Step 4.2.1

Factor $0.5$ out of $- 0.5$ .

$\frac{0.5 (- 1) \frac{1}{- 0.5} + (1 - 1.5) \cdot 1}{(1 - 1.5) \cdot 1.5 + (1 - 1.5) \cdot - 2}$

Step 4.2.2

Factor $0.5$ out of $- 0.5$ .

$\frac{0.5 \cdot - 1 \frac{1}{0.5 \cdot - 1} + (1 - 1.5) \cdot 1}{(1 - 1.5) \cdot 1.5 + (1 - 1.5) \cdot - 2}$

Step 4.2.3

Cancel the common factor.

$\frac{0.5 \cdot - 1 \frac{1}{0.5 \cdot - 1} + (1 - 1.5) \cdot 1}{(1 - 1.5) \cdot 1.5 + (1 - 1.5) \cdot - 2}$

Step 4.2.4

Rewrite the expression.

$\frac{- 1 (\frac{1}{- 1}) + (1 - 1.5) \cdot 1}{(1 - 1.5) \cdot 1.5 + (1 - 1.5) \cdot - 2}$

Step 4.3

Divide $1$ by $- 1$ .

$\frac{- 1 \cdot - 1 + (1 - 1.5) \cdot 1}{(1 - 1.5) \cdot 1.5 + (1 - 1.5) \cdot - 2}$

Step 4.4

Multiply $- 1$ by $- 1$ .

$\frac{1 + (1 - 1.5) \cdot 1}{(1 - 1.5) \cdot 1.5 + (1 - 1.5) \cdot - 2}$

Step 4.5

Subtract $1.5$ from $1$ .

$\frac{1 - 0.5 \cdot 1}{(1 - 1.5) \cdot 1.5 + (1 - 1.5) \cdot - 2}$

Step 4.6

Multiply $- 0.5$ by $1$ .

$\frac{1 - 0.5}{(1 - 1.5) \cdot 1.5 + (1 - 1.5) \cdot - 2}$

Step 4.7

Subtract $0.5$ from $1$ .

$\frac{0.5}{(1 - 1.5) \cdot 1.5 + (1 - 1.5) \cdot - 2}$

Step 5

Simplify the denominator.

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Step 5.1

Subtract $1.5$ from $1$ .

$\frac{0.5}{- 0.5 \cdot 1.5 + (1 - 1.5) \cdot - 2}$

Step 5.2

Multiply $- 0.5$ by $1.5$ .

$\frac{0.5}{- 0.75 + (1 - 1.5) \cdot - 2}$

Step 5.3

Subtract $1.5$ from $1$ .

$\frac{0.5}{- 0.75 - 0.5 \cdot - 2}$

Step 5.4

Multiply $- 0.5$ by $- 2$ .

$\frac{0.5}{- 0.75 + 1}$

Step 5.5

Add $- 0.75$ and $1$ .

$\frac{0.5}{0.25}$

Step 6

Divide $0.5$ by $0.25$ .

$2$