Basic Math Examples

$\frac{80.999 - 81}{\sqrt{80.999} - 9}$

Step 1

Subtract $81$ from $80.999$ .

$\frac{- 0.001}{\sqrt{80.999} - 9}$

Step 2

Move the negative in front of the fraction.

$- \frac{0.001}{\sqrt{80.999} - 9}$

Step 3

Multiply $\frac{0.001}{\sqrt{80.999} - 9}$ by $\frac{\sqrt{80.999} + 9}{\sqrt{80.999} + 9}$ .

$- (\frac{0.001}{\sqrt{80.999} - 9} \cdot \frac{\sqrt{80.999} + 9}{\sqrt{80.999} + 9})$

Step 4

Multiply $\frac{0.001}{\sqrt{80.999} - 9}$ by $\frac{\sqrt{80.999} + 9}{\sqrt{80.999} + 9}$ .

$- \frac{0.001 (\sqrt{80.999} + 9)}{(\sqrt{80.999} - 9) (\sqrt{80.999} + 9)}$

Step 5

Expand the denominator using the FOIL method.

$- \frac{0.001 (\sqrt{80.999} + 9)}{{\sqrt{80.999}}^{2} + \sqrt{80.999} \cdot 9 - 9 \sqrt{80.999} - 81}$

Step 6

Simplify.

$- \frac{0.001 (\sqrt{80.999} + 9)}{- 0.001}$

Step 7

Cancel the common factor of $0.001$ and $- 0.001$ .

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Step 7.1

Rewrite $0.001$ as $- 1 (- 0.001)$ .

$- \frac{- 1 (- 0.001) (\sqrt{80.999} + 9)}{- 0.001}$

Step 7.2

Cancel the common factor.

$- \frac{- 1 \cdot - 0.001 (\sqrt{80.999} + 9)}{- 0.001}$

Step 7.3

Divide $- (\sqrt{80.999} + 9)$ by $1$ .

$- - (\sqrt{80.999} + 9)$

Step 8

Apply the distributive property.

$- (- \sqrt{80.999} - 1 \cdot 9)$

Step 9

Multiply $- 1$ by $9$ .

$- (- \sqrt{80.999} - 9)$

Step 10

Apply the distributive property.

$- - \sqrt{80.999} - - 9$

Step 11

Multiply $- - \sqrt{80.999}$ .

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Step 11.1

Multiply $- 1$ by $- 1$ .

$1 \sqrt{80.999} - - 9$

Step 11.2

Multiply $\sqrt{80.999}$ by $1$ .

$\sqrt{80.999} - - 9$

Step 12

Multiply $- 1$ by $- 9$ .

$\sqrt{80.999} + 9$

Step 13

The result can be shown in multiple forms.

Exact Form:

$\sqrt{80.999} + 9$

Decimal Form:

$17.99994444 \dots$