Divide x^3-1÷(x+2)

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

Step 1

Rewrite the division as a fraction.

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

Step 2

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

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

Step 3

Combine the numerators over the common denominator.

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

Step 4

Simplify the numerator.

Apply the distributive property.

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

Multiply $x^{3}$ by $x$ by adding the exponents.

Multiply $x^{3}$ by $x$ .

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

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

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

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

Add $3$ and $1$ .

$\frac{x^{4} + x^{3} \cdot 2 - 1}{x + 2}$

Move $2$ to the left of $x^{3}$ .

$\frac{x^{4} + 2 x^{3} - 1}{x + 2}$