Simplify 5/2-1/(x^3)

$\frac{5}{2} - \frac{1}{x^{3}}$

Step 1

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

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

Step 2

To write $- \frac{1}{x^{3}}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 3

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

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

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

Multiply $\frac{1}{x^{3}}$ by $\frac{2}{2}$ .

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

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

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

Step 4

Combine the numerators over the common denominator.

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