Calculus Examples

$\frac{3.99 - 4}{\sqrt{3.99} - 2}$

Step 1

Subtract $4$ from $3.99$ .

$\frac{- 0.01}{\sqrt{3.99} - 2}$

Step 2

Move the negative in front of the fraction.

$- \frac{0.01}{\sqrt{3.99} - 2}$

Step 3

Multiply $\frac{0.01}{\sqrt{3.99} - 2}$ by $\frac{\sqrt{3.99} + 2}{\sqrt{3.99} + 2}$ .

$- (\frac{0.01}{\sqrt{3.99} - 2} \cdot \frac{\sqrt{3.99} + 2}{\sqrt{3.99} + 2})$

Step 4

Multiply $\frac{0.01}{\sqrt{3.99} - 2}$ by $\frac{\sqrt{3.99} + 2}{\sqrt{3.99} + 2}$ .

$- \frac{0.01 (\sqrt{3.99} + 2)}{(\sqrt{3.99} - 2) (\sqrt{3.99} + 2)}$

Step 5

Expand the denominator using the FOIL method.

$- \frac{0.01 (\sqrt{3.99} + 2)}{{\sqrt{3.99}}^{2} + \sqrt{3.99} \cdot 2 - 2 \sqrt{3.99} - 4}$

Step 6

Simplify.

$- \frac{0.01 (\sqrt{3.99} + 2)}{- 0.01}$

Step 7

Cancel the common factor of $0.01$ and $- 0.01$ .

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Step 7.1

Rewrite $0.01$ as $- 1 (- 0.01)$ .

$- \frac{- 1 (- 0.01) (\sqrt{3.99} + 2)}{- 0.01}$

Step 7.2

Cancel the common factor.

$- \frac{- 1 \cdot - 0.01 (\sqrt{3.99} + 2)}{- 0.01}$

Step 7.3

Divide $- (\sqrt{3.99} + 2)$ by $1$ .

$- - (\sqrt{3.99} + 2)$

Step 8

Apply the distributive property.

$- (- \sqrt{3.99} - 1 \cdot 2)$

Step 9

Multiply $- 1$ by $2$ .

$- (- \sqrt{3.99} - 2)$

Step 10

Apply the distributive property.

$- - \sqrt{3.99} - - 2$

Step 11

Multiply $- - \sqrt{3.99}$ .

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Step 11.1

Multiply $- 1$ by $- 1$ .

$1 \sqrt{3.99} - - 2$

Step 11.2

Multiply $\sqrt{3.99}$ by $1$ .

$\sqrt{3.99} - - 2$

Step 12

Multiply $- 1$ by $- 2$ .

$\sqrt{3.99} + 2$

Step 13

The result can be shown in multiple forms.

Exact Form:

$\sqrt{3.99} + 2$

Decimal Form:

$3.99749843 \dots$