Simplify x/(y^3)+1/(x^2y^3)

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

To write $\frac{x}{y^{3}}$ as a fraction with a common denominator, multiply by $\frac{x^{2}}{x^{2}}$ .

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

Write each expression with a common denominator of $y^{3} x^{2}$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{x}{y^{3}}$ by $\frac{x^{2}}{x^{2}}$ .

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

Reorder the factors of $x^{2} y^{3}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

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

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

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

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

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

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

Add $1$ and $2$ .

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

Rewrite $1$ as $1^{3}$ .

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

Since both terms are perfect cubes, factor using the sum of cubes formula, $a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})$ where $a = x$ and $b = 1$ .

$\frac{(x + 1) (x^{2} - x \cdot 1 + 1^{2})}{y^{3} x^{2}}$

Simplify.

Multiply $- 1$ by $1$ .

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

One to any power is one.

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

Simplify x/(y^3)+1/(x^2y^3)

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