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

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

Step 1

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

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

Step 2

To write $- \frac{1}{5 x^{3}}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

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

Step 3

Write each expression with a common denominator of $20 x^{3}$ , by multiplying each by an appropriate factor of $1$ .

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

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

Multiply $5$ by $4$ .

$\frac{5 x (5 x^{3})}{20 x^{3}} - \frac{1}{5 x^{3}} \cdot \frac{4}{4}$

Multiply $\frac{1}{5 x^{3}}$ by $\frac{4}{4}$ .

$\frac{5 x (5 x^{3})}{20 x^{3}} - \frac{4}{5 x^{3} \cdot 4}$

Multiply $4$ by $5$ .

$\frac{5 x (5 x^{3})}{20 x^{3}} - \frac{4}{20 x^{3}}$

Step 4

Combine the numerators over the common denominator.

$\frac{5 x (5 x^{3}) - 4}{20 x^{3}}$

Step 5

Simplify the numerator.

Multiply $5$ by $5$ .

$\frac{25 x \cdot x^{3} - 4}{20 x^{3}}$

Multiply $x$ by $x^{3}$ by adding the exponents.

Move $x^{3}$ .

$\frac{25 (x^{3} x) - 4}{20 x^{3}}$

Multiply $x^{3}$ by $x$ .

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

$\frac{25 (x^{3} x^{1}) - 4}{20 x^{3}}$

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

$\frac{25 x^{3 + 1} - 4}{20 x^{3}}$

Add $3$ and $1$ .

$\frac{25 x^{4} - 4}{20 x^{3}}$

Rewrite $25 x^{4}$ as ${(5 x^{2})}^{2}$ .

$\frac{{(5 x^{2})}^{2} - 4}{20 x^{3}}$

Rewrite $4$ as $2^{2}$ .

$\frac{{(5 x^{2})}^{2} - 2^{2}}{20 x^{3}}$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 5 x^{2}$ and $b = 2$ .

$\frac{(5 x^{2} + 2) (5 x^{2} - 2)}{20 x^{3}}$

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

Related Questions

Support LCMGCF.com by disabling your adblocker.