Simplify y/(x^2)+y/(x^3)

$\frac{y}{x^{2}} + \frac{y}{x^{3}}$

Step 1

To write $\frac{y}{x^{2}}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{y}{x^{2}} \cdot \frac{x}{x} + \frac{y}{x^{3}}$

Step 2

Write each expression with a common denominator of $x^{3}$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{y}{x^{2}}$ by $\frac{x}{x}$ .

$\frac{y x}{x^{2} x} + \frac{y}{x^{3}}$

Multiply $x^{2}$ by $x$ by adding the exponents.

Multiply $x^{2}$ by $x$ .

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

$\frac{y x}{x^{2} x^{1}} + \frac{y}{x^{3}}$

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

$\frac{y x}{x^{2 + 1}} + \frac{y}{x^{3}}$

Add $2$ and $1$ .

$\frac{y x}{x^{3}} + \frac{y}{x^{3}}$

Step 3

Combine the numerators over the common denominator.

$\frac{y x + y}{x^{3}}$

Step 4

Factor $y$ out of $y x + y$ .

Factor $y$ out of $y x$ .

$\frac{y (x) + y}{x^{3}}$

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

$\frac{y (x) + y^{1}}{x^{3}}$

Factor $y$ out of $y^{1}$ .

$\frac{y (x) + y \cdot 1}{x^{3}}$

Factor $y$ out of $y (x) + y \cdot 1$ .

$\frac{y (x + 1)}{x^{3}}$