Algebra Examples

$\frac{11}{b - 7} - \frac{2 b - 3}{b - 7}$

Step 1

Combine the numerators over the common denominator.

$\frac{11 - (2 b - 3)}{b - 7}$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$\frac{11 - (2 b) - - 3}{b - 7}$

Step 2.2

Multiply $2$ by $- 1$ .

$\frac{11 - 2 b - - 3}{b - 7}$

Step 2.3

Multiply $- 1$ by $- 3$ .

$\frac{11 - 2 b + 3}{b - 7}$

$\frac{11 - 2 b + 3}{b - 7}$

Step 3

Simplify terms.

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Step 3.1

Add $11$ and $3$ .

$\frac{- 2 b + 14}{b - 7}$

Step 3.2

Factor $2$ out of $- 2 b + 14$ .

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Step 3.2.1

Factor $2$ out of $- 2 b$ .

$\frac{2 (- b) + 14}{b - 7}$

Step 3.2.2

Factor $2$ out of $14$ .

$\frac{2 (- b) + 2 (7)}{b - 7}$

Step 3.2.3

Factor $2$ out of $2 (- b) + 2 (7)$ .

$\frac{2 (- b + 7)}{b - 7}$

$\frac{2 (- b + 7)}{b - 7}$

Step 3.3

Cancel the common factor of $- b + 7$ and $b - 7$ .

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Step 3.3.1

Factor $- 1$ out of $- b$ .

$\frac{2 (- (b) + 7)}{b - 7}$

Step 3.3.2

Rewrite $7$ as $- 1 (- 7)$ .

$\frac{2 (- (b) - 1 (- 7))}{b - 7}$

Step 3.3.3

Factor $- 1$ out of $- (b) - 1 (- 7)$ .

$\frac{2 (- (b - 7))}{b - 7}$

Step 3.3.4

Rewrite $- (b - 7)$ as $- 1 (b - 7)$ .

$\frac{2 (- 1 (b - 7))}{b - 7}$

Step 3.3.5

Cancel the common factor.

$\frac{2 (- 1 (b - 7))}{b - 7}$

Step 3.3.6

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

$2 \cdot (- 1)$

$2 \cdot (- 1)$

Step 3.4

Multiply $2$ by $- 1$ .

$- 2$

$- 2$

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