Simplify 1/(12y^4)+(y-4)/(4y^5)

$\frac{1}{12 y^{4}} + \frac{y - 4}{4 y^{5}}$

To write $\frac{1}{12 y^{4}}$ as a fraction with a common denominator, multiply by $\frac{y}{y}$ .

$\frac{1}{12 y^{4}} \cdot \frac{y}{y} + \frac{y - 4}{4 y^{5}}$

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

$\frac{1}{12 y^{4}} \cdot \frac{y}{y} + \frac{y - 4}{4 y^{5}} \cdot \frac{3}{3}$

Write each expression with a common denominator of $12 y^{5}$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{12 y^{4}}$ by $\frac{y}{y}$ .

$\frac{y}{12 y^{4} y} + \frac{y - 4}{4 y^{5}} \cdot \frac{3}{3}$

Raise $y$ to the power of $1$ .

$\frac{y}{12 (y^{1} y^{4})} + \frac{y - 4}{4 y^{5}} \cdot \frac{3}{3}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{y}{12 y^{1 + 4}} + \frac{y - 4}{4 y^{5}} \cdot \frac{3}{3}$

Add $1$ and $4$ .

$\frac{y}{12 y^{5}} + \frac{y - 4}{4 y^{5}} \cdot \frac{3}{3}$

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

$\frac{y}{12 y^{5}} + \frac{(y - 4) \cdot 3}{4 y^{5} \cdot 3}$

Multiply $3$ by $4$ .

$\frac{y}{12 y^{5}} + \frac{(y - 4) \cdot 3}{12 y^{5}}$

Combine the numerators over the common denominator.

$\frac{y + (y - 4) \cdot 3}{12 y^{5}}$

Simplify the numerator.

Apply the distributive property.

$\frac{y + y \cdot 3 - 4 \cdot 3}{12 y^{5}}$

Move $3$ to the left of $y$ .

$\frac{y + 3 \cdot y - 4 \cdot 3}{12 y^{5}}$

Multiply $- 4$ by $3$ .

$\frac{y + 3 \cdot y - 12}{12 y^{5}}$

Add $y$ and $3 y$ .

$\frac{4 y - 12}{12 y^{5}}$

Factor $4$ out of $4 y - 12$ .

Factor $4$ out of $4 y$ .

$\frac{4 (y) - 12}{12 y^{5}}$

Factor $4$ out of $- 12$ .

$\frac{4 y + 4 \cdot - 3}{12 y^{5}}$

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

$\frac{4 (y - 3)}{12 y^{5}}$

Cancel the common factors.

Factor $4$ out of $12 y^{5}$ .

$\frac{4 (y - 3)}{4 (3 y^{5})}$

Cancel the common factor.

$\frac{4 (y - 3)}{4 (3 y^{5})}$

Rewrite the expression.

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