Algebra Examples

$\frac{22 w + 11}{8 w^{2} - 6 w} - \frac{3}{2 w}$

Step 1

Simplify each term.

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Step 1.1

Factor $11$ out of $22 w + 11$ .

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Step 1.1.1

Factor $11$ out of $22 w$ .

$\frac{11 (2 w) + 11}{8 w^{2} - 6 w} - \frac{3}{2 w}$

Step 1.1.2

Factor $11$ out of $11$ .

$\frac{11 (2 w) + 11 (1)}{8 w^{2} - 6 w} - \frac{3}{2 w}$

Step 1.1.3

Factor $11$ out of $11 (2 w) + 11 (1)$ .

$\frac{11 (2 w + 1)}{8 w^{2} - 6 w} - \frac{3}{2 w}$

Step 1.2

Factor $2 w$ out of $8 w^{2} - 6 w$ .

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Step 1.2.1

Factor $2 w$ out of $8 w^{2}$ .

$\frac{11 (2 w + 1)}{2 w (4 w) - 6 w} - \frac{3}{2 w}$

Step 1.2.2

Factor $2 w$ out of $- 6 w$ .

$\frac{11 (2 w + 1)}{2 w (4 w) + 2 w (- 3)} - \frac{3}{2 w}$

Step 1.2.3

Factor $2 w$ out of $2 w (4 w) + 2 w (- 3)$ .

$\frac{11 (2 w + 1)}{2 w (4 w - 3)} - \frac{3}{2 w}$

Step 2

To write $- \frac{3}{2 w}$ as a fraction with a common denominator, multiply by $\frac{4 w - 3}{4 w - 3}$ .

$\frac{11 (2 w + 1)}{2 w (4 w - 3)} - \frac{3}{2 w} \cdot \frac{4 w - 3}{4 w - 3}$

Step 3

Simplify terms.

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Step 3.1

Multiply $\frac{3}{2 w}$ by $\frac{4 w - 3}{4 w - 3}$ .

$\frac{11 (2 w + 1)}{2 w (4 w - 3)} - \frac{3 (4 w - 3)}{2 w (4 w - 3)}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{11 (2 w + 1) - 3 (4 w - 3)}{2 w (4 w - 3)}$

Step 4

Simplify the numerator.

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Step 4.1

Apply the distributive property.

$\frac{11 (2 w) + 11 \cdot 1 - 3 (4 w - 3)}{2 w (4 w - 3)}$

Step 4.2

Multiply $2$ by $11$ .

$\frac{22 w + 11 \cdot 1 - 3 (4 w - 3)}{2 w (4 w - 3)}$

Step 4.3

Multiply $11$ by $1$ .

$\frac{22 w + 11 - 3 (4 w - 3)}{2 w (4 w - 3)}$

Step 4.4

Apply the distributive property.

$\frac{22 w + 11 - 3 (4 w) - 3 \cdot - 3}{2 w (4 w - 3)}$

Step 4.5

Multiply $4$ by $- 3$ .

$\frac{22 w + 11 - 12 w - 3 \cdot - 3}{2 w (4 w - 3)}$

Step 4.6

Multiply $- 3$ by $- 3$ .

$\frac{22 w + 11 - 12 w + 9}{2 w (4 w - 3)}$

Step 4.7

Subtract $12 w$ from $22 w$ .

$\frac{10 w + 11 + 9}{2 w (4 w - 3)}$

Step 4.8

Add $11$ and $9$ .

$\frac{10 w + 20}{2 w (4 w - 3)}$

Step 4.9

Factor $10$ out of $10 w + 20$ .

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Step 4.9.1

Factor $10$ out of $10 w$ .

$\frac{10 (w) + 20}{2 w (4 w - 3)}$

Step 4.9.2

Factor $10$ out of $20$ .

$\frac{10 w + 10 \cdot 2}{2 w (4 w - 3)}$

Step 4.9.3

Factor $10$ out of $10 w + 10 \cdot 2$ .

$\frac{10 (w + 2)}{2 w (4 w - 3)}$

Step 5

Cancel the common factor of $10$ and $2$ .

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Step 5.1

Factor $2$ out of $10 (w + 2)$ .

$\frac{2 (5 (w + 2))}{2 w (4 w - 3)}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $2$ out of $2 w (4 w - 3)$ .

$\frac{2 (5 (w + 2))}{2 (w (4 w - 3))}$

Step 5.2.2

Cancel the common factor.

$\frac{2 (5 (w + 2))}{2 (w (4 w - 3))}$

Step 5.2.3

Rewrite the expression.

$\frac{5 (w + 2)}{w (4 w - 3)}$