Simplify y-1/(y^2)

$y - \frac{1}{y^{2}}$

Step 1

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

$\frac{y \cdot y^{2}}{y^{2}} - \frac{1}{y^{2}}$

Step 2

Combine the numerators over the common denominator.

$\frac{y \cdot y^{2} - 1}{y^{2}}$

Step 3

Simplify the numerator.

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

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

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

$\frac{y^{1} y^{2} - 1}{y^{2}}$

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

$\frac{y^{1 + 2} - 1}{y^{2}}$

Add $1$ and $2$ .

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

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

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

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

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

Simplify.

Multiply $y$ by $1$ .

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

One to any power is one.

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

Simplify y-1/(y^2)

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