Simplify (17k+3)/(8k+4)+(3k+7)/(8k+4)

$\frac{17 k + 3}{8 k + 4} + \frac{3 k + 7}{8 k + 4}$

Step 1

Combine the numerators over the common denominator.

$\frac{17 k + 3 + 3 k + 7}{8 k + 4}$

Step 2

Add $17 k$ and $3 k$ .

$\frac{20 k + 3 + 7}{8 k + 4}$

Step 3

Add $3$ and $7$ .

$\frac{20 k + 10}{8 k + 4}$

Step 4

Cancel the common factor of $20 k + 10$ and $8 k + 4$ .

Factor $2$ out of $20 k$ .

$\frac{2 (10 k) + 10}{8 k + 4}$

Factor $2$ out of $10$ .

$\frac{2 (10 k) + 2 (5)}{8 k + 4}$

Factor $2$ out of $2 (10 k) + 2 (5)$ .

$\frac{2 (10 k + 5)}{8 k + 4}$

Cancel the common factors.

Factor $2$ out of $8 k$ .

$\frac{2 (10 k + 5)}{2 (4 k) + 4}$

Factor $2$ out of $4$ .

$\frac{2 (10 k + 5)}{2 (4 k) + 2 (2)}$

Factor $2$ out of $2 (4 k) + 2 (2)$ .

$\frac{2 (10 k + 5)}{2 (4 k + 2)}$

Cancel the common factor.

$\frac{2 (10 k + 5)}{2 (4 k + 2)}$

Rewrite the expression.

$\frac{10 k + 5}{4 k + 2}$

Step 5

Factor $5$ out of $10 k + 5$ .

Factor $5$ out of $10 k$ .

$\frac{5 (2 k) + 5}{4 k + 2}$

Factor $5$ out of $5$ .

$\frac{5 (2 k) + 5 (1)}{4 k + 2}$

Factor $5$ out of $5 (2 k) + 5 (1)$ .

$\frac{5 (2 k + 1)}{4 k + 2}$

Step 6

Factor $2$ out of $4 k + 2$ .

Factor $2$ out of $4 k$ .

$\frac{5 (2 k + 1)}{2 (2 k) + 2}$

Factor $2$ out of $2$ .

$\frac{5 (2 k + 1)}{2 (2 k) + 2 (1)}$

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

$\frac{5 (2 k + 1)}{2 (2 k + 1)}$

Step 7

Cancel the common factor of $2 k + 1$ .

Cancel the common factor.

$\frac{5 (2 k + 1)}{2 (2 k + 1)}$

Rewrite the expression.

$\frac{5}{2}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{2}$

Decimal Form:

$2.5$

Mixed Number Form:

$2 \frac{1}{2}$

Simplify (17k+3)/(8k+4)+(3k+7)/(8k+4)

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