Simplify (6y-4)/(y^2-5)-(3y+1)/(y^2-5)

$\frac{6 y - 4}{y^{2} - 5} - \frac{3 y + 1}{y^{2} - 5}$

Step 1

Combine the numerators over the common denominator.

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

Step 2

Simplify each term.

Apply the distributive property.

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

Multiply $3$ by $- 1$ .

$\frac{6 y - 4 - 3 y - 1 \cdot 1}{y^{2} - 5}$

Multiply $- 1$ by $1$ .

$\frac{6 y - 4 - 3 y - 1}{y^{2} - 5}$

Step 3

Simplify by adding terms.

Subtract $3 y$ from $6 y$ .

$\frac{3 y - 4 - 1}{y^{2} - 5}$

Subtract $1$ from $- 4$ .

$\frac{3 y - 5}{y^{2} - 5}$