Algebra Examples

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

Step 1

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

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

Step 2

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

Tap for more steps...

Step 2.1

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

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

Step 2.2

Multiply $2$ by $4$ .

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

Step 2.3

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

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

Step 2.4

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

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

Step 2.5

Add $1$ and $2$ .

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

Step 3

Combine the numerators over the common denominator.

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

Step 4

Simplify the numerator.

Tap for more steps...

Step 4.1

Apply the distributive property.

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

Step 4.2

Move $2$ to the left of $x$ .

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

Step 4.3

Multiply $- 1$ by $2$ .

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

Step 4.4

Apply the distributive property.

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

Step 4.5

Multiply $x$ by $x$ by adding the exponents.

Tap for more steps...

Step 4.5.1

Move $x$ .

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

Step 4.5.2

Multiply $x$ by $x$ .

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

Step 4.6

Subtract $2 x$ from $2 x$ .

$\frac{1 + 2 x^{2} + 0}{8 x^{3}}$

Step 4.7

Add $1 + 2 x^{2}$ and $0$ .

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