Algebra Examples

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

Step 1

To write $- 6 x$ as a fraction with a common denominator, multiply by $\frac{3 x^{2}}{3 x^{2}}$ .

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

Step 2

Simplify terms.

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Step 2.1

Combine $- 6 x$ and $\frac{3 x^{2}}{3 x^{2}}$ .

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

Step 2.2

Combine the numerators over the common denominator.

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

Step 3

Simplify the numerator.

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Step 3.1

Rewrite using the commutative property of multiplication.

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

Step 3.2

Multiply $x$ by $x^{2}$ by adding the exponents.

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Step 3.2.1

Move $x^{2}$ .

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

Step 3.2.2

Multiply $x^{2}$ by $x$ .

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Step 3.2.2.1

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

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

Step 3.2.2.2

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

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

Step 3.2.3

Add $2$ and $1$ .

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

Step 3.3

Multiply $- 6$ by $3$ .

$\frac{5 - 18 x^{3}}{3 x^{2}}$