Simplify 5/3-3/(4x^3)

$\frac{5}{3} - \frac{3}{4 x^{3}}$

Step 1

To write $\frac{5}{3}$ as a fraction with a common denominator, multiply by $\frac{4 x^{3}}{4 x^{3}}$ .

$\frac{5}{3} \cdot \frac{4 x^{3}}{4 x^{3}} - \frac{3}{4 x^{3}}$

Step 2

To write $- \frac{3}{4 x^{3}}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{5}{3} \cdot \frac{4 x^{3}}{4 x^{3}} - \frac{3}{4 x^{3}} \cdot \frac{3}{3}$

Step 3

Write each expression with a common denominator of $12 x^{3}$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{5}{3}$ by $\frac{4 x^{3}}{4 x^{3}}$ .

$\frac{5 (4 x^{3})}{3 (4 x^{3})} - \frac{3}{4 x^{3}} \cdot \frac{3}{3}$

Multiply $4$ by $3$ .

$\frac{5 (4 x^{3})}{12 x^{3}} - \frac{3}{4 x^{3}} \cdot \frac{3}{3}$

Multiply $\frac{3}{4 x^{3}}$ by $\frac{3}{3}$ .

$\frac{5 (4 x^{3})}{12 x^{3}} - \frac{3 \cdot 3}{4 x^{3} \cdot 3}$

Multiply $3$ by $4$ .

$\frac{5 (4 x^{3})}{12 x^{3}} - \frac{3 \cdot 3}{12 x^{3}}$

Step 4

Combine the numerators over the common denominator.

$\frac{5 (4 x^{3}) - 3 \cdot 3}{12 x^{3}}$

Step 5

Simplify the numerator.

Multiply $5$ by $4$ .

$\frac{20 x^{3} - 3 \cdot 3}{12 x^{3}}$

Multiply $- 3$ by $3$ .

$\frac{20 x^{3} - 9}{12 x^{3}}$