Basic Math Examples

$(r + 2 \cdot (2 r) - 9 - r^{2} + 17 r + 30) \div r + 2$

Step 1

Simplify by adding terms.

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Step 1.1

Add $r$ and $17 r$ .

$(18 r + 2 \cdot (2 r) - 9 - r^{2} + 30) \div r + 2$

Step 1.2

Add $- 9$ and $30$ .

$(18 r + 2 \cdot (2 r) - r^{2} + 21) \div r + 2$

Step 2

Simplify each term.

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Step 2.1

Rewrite the division as a fraction.

$\frac{18 r + 2 \cdot (2 r) - r^{2} + 21}{r} + 2$

Step 2.2

Simplify the numerator.

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Step 2.2.1

Multiply $2$ by $2$ .

$\frac{18 r + 4 r - r^{2} + 21}{r} + 2$

Step 2.2.2

Add $18 r$ and $4 r$ .

$\frac{22 r - r^{2} + 21}{r} + 2$

Step 2.2.3

Reorder terms.

$\frac{- r^{2} + 22 r + 21}{r} + 2$

Step 3

To write $2$ as a fraction with a common denominator, multiply by $\frac{r}{r}$ .

$\frac{- r^{2} + 22 r + 21}{r} + \frac{2 r}{r}$

Step 4

Combine the numerators over the common denominator.

$\frac{- r^{2} + 22 r + 21 + 2 r}{r}$

Step 5

Add $22 r$ and $2 r$ .

$\frac{- r^{2} + 24 r + 21}{r}$

Step 6

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

$\frac{- (r^{2}) + 24 r + 21}{r}$

Step 7

Factor $- 1$ out of $24 r$ .

$\frac{- (r^{2}) - (- 24 r) + 21}{r}$

Step 8

Factor $- 1$ out of $- (r^{2}) - (- 24 r)$ .

$\frac{- (r^{2} - 24 r) + 21}{r}$

Step 9

Rewrite $21$ as $- 1 (- 21)$ .

$\frac{- (r^{2} - 24 r) - 1 (- 21)}{r}$

Step 10

Factor $- 1$ out of $- (r^{2} - 24 r) - 1 (- 21)$ .

$\frac{- (r^{2} - 24 r - 21)}{r}$

Step 11

Simplify the expression.

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Step 11.1

Rewrite $- (r^{2} - 24 r - 21)$ as $- 1 (r^{2} - 24 r - 21)$ .

$\frac{- 1 (r^{2} - 24 r - 21)}{r}$

Step 11.2

Move the negative in front of the fraction.

$- \frac{r^{2} - 24 r - 21}{r}$