Simplify (3y)/(y-4)-(11y)/(4y-16)

$\frac{3 y}{y - 4} - \frac{11 y}{4 y - 16}$

Step 1

Factor $4$ out of $4 y - 16$ .

Factor $4$ out of $4 y$ .

$\frac{3 y}{y - 4} - \frac{11 y}{4 (y) - 16}$

Factor $4$ out of $- 16$ .

$\frac{3 y}{y - 4} - \frac{11 y}{4 y + 4 \cdot - 4}$

Factor $4$ out of $4 y + 4 \cdot - 4$ .

$\frac{3 y}{y - 4} - \frac{11 y}{4 (y - 4)}$

Step 2

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

$\frac{3 y}{y - 4} \cdot \frac{4}{4} - \frac{11 y}{4 (y - 4)}$

Step 3

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

Multiply $\frac{3 y}{y - 4}$ by $\frac{4}{4}$ .

$\frac{3 y \cdot 4}{(y - 4) \cdot 4} - \frac{11 y}{4 (y - 4)}$

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

$\frac{3 y \cdot 4}{4 (y - 4)} - \frac{11 y}{4 (y - 4)}$

Step 4

Combine the numerators over the common denominator.

$\frac{3 y \cdot 4 - 11 y}{4 (y - 4)}$

Step 5

Simplify the numerator.

Factor $y$ out of $3 y \cdot 4 - 11 y$ .

Factor $y$ out of $3 y \cdot 4$ .

$\frac{y (3 \cdot 4) - 11 y}{4 (y - 4)}$

Factor $y$ out of $- 11 y$ .

$\frac{y (3 \cdot 4) + y \cdot - 11}{4 (y - 4)}$

Factor $y$ out of $y (3 \cdot 4) + y \cdot - 11$ .

$\frac{y (3 \cdot 4 - 11)}{4 (y - 4)}$

Multiply $3$ by $4$ .

$\frac{y (12 - 11)}{4 (y - 4)}$

Subtract $11$ from $12$ .

$\frac{y \cdot 1}{4 (y - 4)}$

Step 6

Multiply $y$ by $1$ .

$\frac{y}{4 (y - 4)}$