Simplify (3k)/(4k)+(k-3)/(5k-4)

$\frac{3 k}{4 k} + \frac{k - 3}{5 k - 4}$

Cancel the common factor of $k$ .

Cancel the common factor.

$\frac{3 k}{4 k} + \frac{k - 3}{5 k - 4}$

Rewrite the expression.

$\frac{3}{4} + \frac{k - 3}{5 k - 4}$

To write $\frac{3}{4}$ as a fraction with a common denominator, multiply by $\frac{5 k - 4}{5 k - 4}$ .

$\frac{3}{4} \cdot \frac{5 k - 4}{5 k - 4} + \frac{k - 3}{5 k - 4}$

To write $\frac{k - 3}{5 k - 4}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{3}{4} \cdot \frac{5 k - 4}{5 k - 4} + \frac{k - 3}{5 k - 4} \cdot \frac{4}{4}$

Write each expression with a common denominator of $4 (5 k - 4)$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{3}{4}$ by $\frac{5 k - 4}{5 k - 4}$ .

$\frac{3 (5 k - 4)}{4 (5 k - 4)} + \frac{k - 3}{5 k - 4} \cdot \frac{4}{4}$

Multiply $\frac{k - 3}{5 k - 4}$ by $\frac{4}{4}$ .

$\frac{3 (5 k - 4)}{4 (5 k - 4)} + \frac{(k - 3) \cdot 4}{(5 k - 4) \cdot 4}$

Reorder the factors of $(5 k - 4) \cdot 4$ .

$\frac{3 (5 k - 4)}{4 (5 k - 4)} + \frac{(k - 3) \cdot 4}{4 (5 k - 4)}$

Combine the numerators over the common denominator.

$\frac{3 (5 k - 4) + (k - 3) \cdot 4}{4 (5 k - 4)}$

Simplify the numerator.

Apply the distributive property.

$\frac{3 (5 k) + 3 \cdot - 4 + (k - 3) \cdot 4}{4 (5 k - 4)}$

Multiply $5$ by $3$ .

$\frac{15 k + 3 \cdot - 4 + (k - 3) \cdot 4}{4 (5 k - 4)}$

Multiply $3$ by $- 4$ .

$\frac{15 k - 12 + (k - 3) \cdot 4}{4 (5 k - 4)}$

Apply the distributive property.

$\frac{15 k - 12 + k \cdot 4 - 3 \cdot 4}{4 (5 k - 4)}$

Move $4$ to the left of $k$ .

$\frac{15 k - 12 + 4 \cdot k - 3 \cdot 4}{4 (5 k - 4)}$

Multiply $- 3$ by $4$ .

$\frac{15 k - 12 + 4 \cdot k - 12}{4 (5 k - 4)}$

Add $15 k$ and $4 k$ .

$\frac{19 k - 12 - 12}{4 (5 k - 4)}$

Subtract $12$ from $- 12$ .

$\frac{19 k - 24}{4 (5 k - 4)}$