Algebra Examples

$\frac{1}{4 x^{2}} - \frac{2 x - 4}{16 x^{3}}$

Step 1

Cancel the common factor of $2 x - 4$ and $16$ .

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Step 1.1

Factor $2$ out of $2 x$ .

$\frac{1}{4 x^{2}} - \frac{2 (x) - 4}{16 x^{3}}$

Step 1.2

Factor $2$ out of $- 4$ .

$\frac{1}{4 x^{2}} - \frac{2 x + 2 \cdot - 2}{16 x^{3}}$

Step 1.3

Factor $2$ out of $2 x + 2 \cdot - 2$ .

$\frac{1}{4 x^{2}} - \frac{2 (x - 2)}{16 x^{3}}$

Step 1.4

Cancel the common factors.

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Step 1.4.1

Factor $2$ out of $16 x^{3}$ .

$\frac{1}{4 x^{2}} - \frac{2 (x - 2)}{2 (8 x^{3})}$

Step 1.4.2

Cancel the common factor.

$\frac{1}{4 x^{2}} - \frac{2 (x - 2)}{2 (8 x^{3})}$

Step 1.4.3

Rewrite the expression.

$\frac{1}{4 x^{2}} - \frac{x - 2}{8 x^{3}}$

Step 2

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

$\frac{1}{4 x^{2}} \cdot \frac{2 x}{2 x} - \frac{x - 2}{8 x^{3}}$

Step 3

Write each expression with a common denominator of $8 x^{3}$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

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

$\frac{2 x}{4 x^{2} (2 x)} - \frac{x - 2}{8 x^{3}}$

Step 3.2

Rewrite using the commutative property of multiplication.

$\frac{2 x}{4 \cdot 2 x^{2} x} - \frac{x - 2}{8 x^{3}}$

Step 3.3

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

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Step 3.3.1

Move $x$ .

$\frac{2 x}{4 \cdot 2 (x \cdot x^{2})} - \frac{x - 2}{8 x^{3}}$

Step 3.3.2

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

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Step 3.3.2.1

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

$\frac{2 x}{4 \cdot 2 (x^{1} x^{2})} - \frac{x - 2}{8 x^{3}}$

Step 3.3.2.2

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

$\frac{2 x}{4 \cdot 2 x^{1 + 2}} - \frac{x - 2}{8 x^{3}}$

Step 3.3.3

Add $1$ and $2$ .

$\frac{2 x}{4 \cdot 2 x^{3}} - \frac{x - 2}{8 x^{3}}$

Step 3.4

Multiply $4$ by $2$ .

$\frac{2 x}{8 x^{3}} - \frac{x - 2}{8 x^{3}}$

Step 4

Combine the numerators over the common denominator.

$\frac{2 x - (x - 2)}{8 x^{3}}$

Step 5

Simplify the numerator.

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Step 5.1

Apply the distributive property.

$\frac{2 x - x - - 2}{8 x^{3}}$

Step 5.2

Multiply $- 1$ by $- 2$ .

$\frac{2 x - x + 2}{8 x^{3}}$

Step 5.3

Subtract $x$ from $2 x$ .

$\frac{x + 2}{8 x^{3}}$