Simplify 5/(x^3)-1/(4x^2)

$\frac{5}{x^{3}} - \frac{1}{4 x^{2}}$

Step 1

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

$\frac{5}{x^{3}} \cdot \frac{4}{4} - \frac{1}{4 x^{2}}$

Step 2

To write $- \frac{1}{4 x^{2}}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{5}{x^{3}} \cdot \frac{4}{4} - \frac{1}{4 x^{2}} \cdot \frac{x}{x}$

Step 3

Write each expression with a common denominator of $4 x^{3}$ , by multiplying each by an appropriate factor of $1$ .

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

$\frac{5 \cdot 4}{x^{3} \cdot 4} - \frac{1}{4 x^{2}} \cdot \frac{x}{x}$

Multiply $\frac{1}{4 x^{2}}$ by $\frac{x}{x}$ .

$\frac{5 \cdot 4}{x^{3} \cdot 4} - \frac{x}{4 x^{2} x}$

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

$\frac{5 \cdot 4}{x^{3} \cdot 4} - \frac{x}{4 (x^{1} x^{2})}$

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

$\frac{5 \cdot 4}{x^{3} \cdot 4} - \frac{x}{4 x^{1 + 2}}$

Add $1$ and $2$ .

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

Reorder the factors of $x^{3} \cdot 4$ .

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Multiply $5$ by $4$ .

$\frac{20 - x}{4 x^{3}}$