Algebra Examples

$\frac{r + 9}{r - 4} - \frac{3 r + 1}{r - 4}$

Step 1

Combine the numerators over the common denominator.

$\frac{r + 9 - (3 r + 1)}{r - 4}$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$\frac{r + 9 - (3 r) - 1 \cdot 1}{r - 4}$

Step 2.2

Multiply $3$ by $- 1$ .

$\frac{r + 9 - 3 r - 1 \cdot 1}{r - 4}$

Step 2.3

Multiply $- 1$ by $1$ .

$\frac{r + 9 - 3 r - 1}{r - 4}$

$\frac{r + 9 - 3 r - 1}{r - 4}$

Step 3

Simplify terms.

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Step 3.1

Subtract $3 r$ from $r$ .

$\frac{- 2 r + 9 - 1}{r - 4}$

Step 3.2

Subtract $1$ from $9$ .

$\frac{- 2 r + 8}{r - 4}$

Step 3.3

Factor $2$ out of $- 2 r + 8$ .

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Step 3.3.1

Factor $2$ out of $- 2 r$ .

$\frac{2 (- r) + 8}{r - 4}$

Step 3.3.2

Factor $2$ out of $8$ .

$\frac{2 (- r) + 2 (4)}{r - 4}$

Step 3.3.3

Factor $2$ out of $2 (- r) + 2 (4)$ .

$\frac{2 (- r + 4)}{r - 4}$

$\frac{2 (- r + 4)}{r - 4}$

Step 3.4

Cancel the common factor of $- r + 4$ and $r - 4$ .

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Step 3.4.1

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

$\frac{2 (- (r) + 4)}{r - 4}$

Step 3.4.2

Rewrite $4$ as $- 1 (- 4)$ .

$\frac{2 (- (r) - 1 (- 4))}{r - 4}$

Step 3.4.3

Factor $- 1$ out of $- (r) - 1 (- 4)$ .

$\frac{2 (- (r - 4))}{r - 4}$

Step 3.4.4

Rewrite $- (r - 4)$ as $- 1 (r - 4)$ .

$\frac{2 (- 1 (r - 4))}{r - 4}$

Step 3.4.5

Cancel the common factor.

$\frac{2 (- 1 (r - 4))}{r - 4}$

Step 3.4.6

Divide $2 \cdot (- 1)$ by $1$ .

$2 \cdot (- 1)$

$2 \cdot (- 1)$

Step 3.5

Multiply $2$ by $- 1$ .

$- 2$

$- 2$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$