Algebra Examples

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

Step 1

To write $- \frac{3}{2 x^{3}}$ as a fraction with a common denominator, multiply by $\frac{4 x}{4 x}$ .

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

Step 2

Write each expression with a common denominator of $8 x^{4}$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.1

Multiply $\frac{3}{2 x^{3}}$ by $\frac{4 x}{4 x}$ .

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

Step 2.2

Multiply $4$ by $2$ .

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

Step 2.3

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

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

Step 2.4

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

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

Step 2.5

Add $1$ and $3$ .

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

Step 3

Combine the numerators over the common denominator.

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

Step 4

Simplify the numerator.

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Step 4.1

Multiply $- 3$ by $4$ .

$\frac{2 x + 1 - 12 x}{8 x^{4}}$

Step 4.2

Subtract $12 x$ from $2 x$ .

$\frac{- 10 x + 1}{8 x^{4}}$

Step 5

Simplify with factoring out.

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Step 5.1

Factor $- 1$ out of $- 10 x$ .

$\frac{- (10 x) + 1}{8 x^{4}}$

Step 5.2

Rewrite $1$ as $- 1 (- 1)$ .

$\frac{- (10 x) - 1 (- 1)}{8 x^{4}}$

Step 5.3

Factor $- 1$ out of $- (10 x) - 1 (- 1)$ .

$\frac{- (10 x - 1)}{8 x^{4}}$

Step 5.4

Simplify the expression.

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Step 5.4.1

Rewrite $- (10 x - 1)$ as $- 1 (10 x - 1)$ .

$\frac{- 1 (10 x - 1)}{8 x^{4}}$

Step 5.4.2

Move the negative in front of the fraction.

$- \frac{10 x - 1}{8 x^{4}}$