Simplify 1/3x^3-1/5x^3

$\frac{1}{3} x^{3} - \frac{1}{5} x^{3}$

Step 1

Simplify each term.

Combine $\frac{1}{3}$ and $x^{3}$ .

$\frac{x^{3}}{3} - \frac{1}{5} x^{3}$

Combine $x^{3}$ and $\frac{1}{5}$ .

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

Step 2

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

$\frac{x^{3}}{3} \cdot \frac{5}{5} - \frac{x^{3}}{5}$

Step 3

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

$\frac{x^{3}}{3} \cdot \frac{5}{5} - \frac{x^{3}}{5} \cdot \frac{3}{3}$

Step 4

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{x^{3}}{3}$ by $\frac{5}{5}$ .

$\frac{x^{3} \cdot 5}{3 \cdot 5} - \frac{x^{3}}{5} \cdot \frac{3}{3}$

Multiply $3$ by $5$ .

$\frac{x^{3} \cdot 5}{15} - \frac{x^{3}}{5} \cdot \frac{3}{3}$

Multiply $\frac{x^{3}}{5}$ by $\frac{3}{3}$ .

$\frac{x^{3} \cdot 5}{15} - \frac{x^{3} \cdot 3}{5 \cdot 3}$

Multiply $5$ by $3$ .

$\frac{x^{3} \cdot 5}{15} - \frac{x^{3} \cdot 3}{15}$

Step 5

Combine the numerators over the common denominator.

$\frac{x^{3} \cdot 5 - x^{3} \cdot 3}{15}$

Step 6

Simplify the numerator.

Factor $x^{3}$ out of $x^{3} \cdot 5 - x^{3} \cdot 3$ .

Factor $x^{3}$ out of $x^{3} \cdot 5$ .

$\frac{x^{3} (5) - x^{3} \cdot 3}{15}$

Factor $x^{3}$ out of $- x^{3} \cdot 3$ .

$\frac{x^{3} (5) + x^{3} (- 1 \cdot 3)}{15}$

Factor $x^{3}$ out of $x^{3} (5) + x^{3} (- 1 \cdot 3)$ .

$\frac{x^{3} (5 - 1 \cdot 3)}{15}$

Multiply $- 1$ by $3$ .

$\frac{x^{3} (5 - 3)}{15}$

Subtract $3$ from $5$ .

$\frac{x^{3} \cdot 2}{15}$

Step 7

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

$\frac{2 x^{3}}{15}$