Simplify 5/(3x^3)-5/2

$\frac{5}{3 x^{3}} - \frac{5}{2}$

Step 1

To write $\frac{5}{3 x^{3}}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{5}{3 x^{3}} \cdot \frac{2}{2} - \frac{5}{2}$

Step 2

To write $- \frac{5}{2}$ as a fraction with a common denominator, multiply by $\frac{3 x^{3}}{3 x^{3}}$ .

$\frac{5}{3 x^{3}} \cdot \frac{2}{2} - \frac{5}{2} \cdot \frac{3 x^{3}}{3 x^{3}}$

Step 3

Write each expression with a common denominator of $6 x^{3}$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{5}{3 x^{3}}$ by $\frac{2}{2}$ .

$\frac{5 \cdot 2}{3 x^{3} \cdot 2} - \frac{5}{2} \cdot \frac{3 x^{3}}{3 x^{3}}$

Multiply $2$ by $3$ .

$\frac{5 \cdot 2}{6 x^{3}} - \frac{5}{2} \cdot \frac{3 x^{3}}{3 x^{3}}$

Multiply $\frac{5}{2}$ by $\frac{3 x^{3}}{3 x^{3}}$ .

$\frac{5 \cdot 2}{6 x^{3}} - \frac{5 (3 x^{3})}{2 (3 x^{3})}$

Multiply $3$ by $2$ .

$\frac{5 \cdot 2}{6 x^{3}} - \frac{5 (3 x^{3})}{6 x^{3}}$

Step 4

Combine the numerators over the common denominator.

$\frac{5 \cdot 2 - 5 (3 x^{3})}{6 x^{3}}$

Step 5

Simplify the numerator.

Factor $5$ out of $5 \cdot 2 - 5 \cdot 3 x^{3}$ .

Factor $5$ out of $5 \cdot 2$ .

$\frac{5 (2) - 5 \cdot 3 x^{3}}{6 x^{3}}$

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

$\frac{5 (2) + 5 (- 1 \cdot 3 x^{3})}{6 x^{3}}$

Factor $5$ out of $5 (2) + 5 (- 1 \cdot 3 x^{3})$ .

$\frac{5 (2 - 1 \cdot 3 x^{3})}{6 x^{3}}$

Multiply $- 1$ by $3$ .

$\frac{5 (2 - 3 x^{3})}{6 x^{3}}$