Algebra Examples

$\frac{5 y + 3}{2 y + 2} - \frac{7 y + 4}{3 y + 3}$

Step 1

Simplify each term.

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Step 1.1

Factor $2$ out of $2 y + 2$ .

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Step 1.1.1

Factor $2$ out of $2 y$ .

$\frac{5 y + 3}{2 (y) + 2} - \frac{7 y + 4}{3 y + 3}$

Step 1.1.2

Factor $2$ out of $2$ .

$\frac{5 y + 3}{2 (y) + 2 (1)} - \frac{7 y + 4}{3 y + 3}$

Step 1.1.3

Factor $2$ out of $2 (y) + 2 (1)$ .

$\frac{5 y + 3}{2 (y + 1)} - \frac{7 y + 4}{3 y + 3}$

Step 1.2

Factor $3$ out of $3 y + 3$ .

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Step 1.2.1

Factor $3$ out of $3 y$ .

$\frac{5 y + 3}{2 (y + 1)} - \frac{7 y + 4}{3 (y) + 3}$

Step 1.2.2

Factor $3$ out of $3$ .

$\frac{5 y + 3}{2 (y + 1)} - \frac{7 y + 4}{3 (y) + 3 (1)}$

Step 1.2.3

Factor $3$ out of $3 (y) + 3 (1)$ .

$\frac{5 y + 3}{2 (y + 1)} - \frac{7 y + 4}{3 (y + 1)}$

Step 2

To write $\frac{5 y + 3}{2 (y + 1)}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{5 y + 3}{2 (y + 1)} \cdot \frac{3}{3} - \frac{7 y + 4}{3 (y + 1)}$

Step 3

To write $- \frac{7 y + 4}{3 (y + 1)}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{5 y + 3}{2 (y + 1)} \cdot \frac{3}{3} - \frac{7 y + 4}{3 (y + 1)} \cdot \frac{2}{2}$

Step 4

Write each expression with a common denominator of $6 (y + 1)$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{5 y + 3}{2 (y + 1)}$ by $\frac{3}{3}$ .

$\frac{(5 y + 3) \cdot 3}{2 (y + 1) \cdot 3} - \frac{7 y + 4}{3 (y + 1)} \cdot \frac{2}{2}$

Step 4.2

Multiply $3$ by $2$ .

$\frac{(5 y + 3) \cdot 3}{6 (y + 1)} - \frac{7 y + 4}{3 (y + 1)} \cdot \frac{2}{2}$

Step 4.3

Multiply $\frac{7 y + 4}{3 (y + 1)}$ by $\frac{2}{2}$ .

$\frac{(5 y + 3) \cdot 3}{6 (y + 1)} - \frac{(7 y + 4) \cdot 2}{3 (y + 1) \cdot 2}$

Step 4.4

Multiply $2$ by $3$ .

$\frac{(5 y + 3) \cdot 3}{6 (y + 1)} - \frac{(7 y + 4) \cdot 2}{6 (y + 1)}$

Step 5

Combine the numerators over the common denominator.

$\frac{(5 y + 3) \cdot 3 - (7 y + 4) \cdot 2}{6 (y + 1)}$

Step 6

Simplify the numerator.

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Step 6.1

Apply the distributive property.

$\frac{5 y \cdot 3 + 3 \cdot 3 - (7 y + 4) \cdot 2}{6 (y + 1)}$

Step 6.2

Multiply $3$ by $5$ .

$\frac{15 y + 3 \cdot 3 - (7 y + 4) \cdot 2}{6 (y + 1)}$

Step 6.3

Multiply $3$ by $3$ .

$\frac{15 y + 9 - (7 y + 4) \cdot 2}{6 (y + 1)}$

Step 6.4

Apply the distributive property.

$\frac{15 y + 9 + (- (7 y) - 1 \cdot 4) \cdot 2}{6 (y + 1)}$

Step 6.5

Multiply $7$ by $- 1$ .

$\frac{15 y + 9 + (- 7 y - 1 \cdot 4) \cdot 2}{6 (y + 1)}$

Step 6.6

Multiply $- 1$ by $4$ .

$\frac{15 y + 9 + (- 7 y - 4) \cdot 2}{6 (y + 1)}$

Step 6.7

Apply the distributive property.

$\frac{15 y + 9 - 7 y \cdot 2 - 4 \cdot 2}{6 (y + 1)}$

Step 6.8

Multiply $2$ by $- 7$ .

$\frac{15 y + 9 - 14 y - 4 \cdot 2}{6 (y + 1)}$

Step 6.9

Multiply $- 4$ by $2$ .

$\frac{15 y + 9 - 14 y - 8}{6 (y + 1)}$

Step 6.10

Subtract $14 y$ from $15 y$ .

$\frac{y + 9 - 8}{6 (y + 1)}$

Step 6.11

Subtract $8$ from $9$ .

$\frac{y + 1}{6 (y + 1)}$

Step 7

Cancel the common factor of $y + 1$ .

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Step 7.1

Cancel the common factor.

$\frac{y + 1}{6 (y + 1)}$

Step 7.2

Rewrite the expression.

$\frac{1}{6}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{6}$

Decimal Form:

$0.1\overline{6}$