Simplify 5/(21k-18)+(7k)/(2k)

$\frac{5}{21 k - 18} + \frac{7 k}{2 k}$

Step 1

Simplify each term.

Factor $3$ out of $21 k - 18$ .

Factor $3$ out of $21 k$ .

$\frac{5}{3 (7 k) - 18} + \frac{7 k}{2 k}$

Factor $3$ out of $- 18$ .

$\frac{5}{3 (7 k) + 3 (- 6)} + \frac{7 k}{2 k}$

Factor $3$ out of $3 (7 k) + 3 (- 6)$ .

$\frac{5}{3 (7 k - 6)} + \frac{7 k}{2 k}$

Cancel the common factor of $k$ .

Cancel the common factor.

$\frac{5}{3 (7 k - 6)} + \frac{7 k}{2 k}$

Rewrite the expression.

$\frac{5}{3 (7 k - 6)} + \frac{7}{2}$

Step 2

To write $\frac{5}{3 (7 k - 6)}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{5}{3 (7 k - 6)} \cdot \frac{2}{2} + \frac{7}{2}$

Step 3

To write $\frac{7}{2}$ as a fraction with a common denominator, multiply by $\frac{3 (7 k - 6)}{3 (7 k - 6)}$ .

$\frac{5}{3 (7 k - 6)} \cdot \frac{2}{2} + \frac{7}{2} \cdot \frac{3 (7 k - 6)}{3 (7 k - 6)}$

Step 4

Write each expression with a common denominator of $6 (7 k - 6)$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{5}{3 (7 k - 6)}$ by $\frac{2}{2}$ .

$\frac{5 \cdot 2}{3 (7 k - 6) \cdot 2} + \frac{7}{2} \cdot \frac{3 (7 k - 6)}{3 (7 k - 6)}$

Multiply $2$ by $3$ .

$\frac{5 \cdot 2}{6 (7 k - 6)} + \frac{7}{2} \cdot \frac{3 (7 k - 6)}{3 (7 k - 6)}$

Multiply $\frac{7}{2}$ by $\frac{3 (7 k - 6)}{3 (7 k - 6)}$ .

$\frac{5 \cdot 2}{6 (7 k - 6)} + \frac{7 (3 (7 k - 6))}{2 (3 (7 k - 6))}$

Multiply $3$ by $2$ .

$\frac{5 \cdot 2}{6 (7 k - 6)} + \frac{7 (3 (7 k - 6))}{6 (7 k - 6)}$

Step 5

Combine the numerators over the common denominator.

$\frac{5 \cdot 2 + 7 (3 (7 k - 6))}{6 (7 k - 6)}$

Step 6

Simplify the numerator.

Multiply $5$ by $2$ .

$\frac{10 + 7 \cdot 3 (7 k - 6)}{6 (7 k - 6)}$

Multiply $7$ by $3$ .

$\frac{10 + 21 (7 k - 6)}{6 (7 k - 6)}$

Apply the distributive property.

$\frac{10 + 21 (7 k) + 21 \cdot - 6}{6 (7 k - 6)}$

Multiply $7$ by $21$ .

$\frac{10 + 147 k + 21 \cdot - 6}{6 (7 k - 6)}$

Multiply $21$ by $- 6$ .

$\frac{10 + 147 k - 126}{6 (7 k - 6)}$

Subtract $126$ from $10$ .

$\frac{147 k - 116}{6 (7 k - 6)}$

Simplify 5/(21k-18)+(7k)/(2k)

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