Algebra Examples

$2 p - \frac{4 p^{2} + 1}{2 p}$

Step 1

To write $2 p$ as a fraction with a common denominator, multiply by $\frac{2 p}{2 p}$ .

$2 p \cdot \frac{2 p}{2 p} - \frac{4 p^{2} + 1}{2 p}$

Step 2

Simplify terms.

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Step 2.1

Combine $2 p$ and $\frac{2 p}{2 p}$ .

$\frac{2 p (2 p)}{2 p} - \frac{4 p^{2} + 1}{2 p}$

Step 2.2

Combine the numerators over the common denominator.

$\frac{2 p (2 p) - (4 p^{2} + 1)}{2 p}$

Step 3

Simplify the numerator.

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Step 3.1

Rewrite using the commutative property of multiplication.

$\frac{2 \cdot 2 p \cdot p - (4 p^{2} + 1)}{2 p}$

Step 3.2

Multiply $p$ by $p$ by adding the exponents.

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Step 3.2.1

Move $p$ .

$\frac{2 \cdot 2 (p \cdot p) - (4 p^{2} + 1)}{2 p}$

Step 3.2.2

Multiply $p$ by $p$ .

$\frac{2 \cdot 2 p^{2} - (4 p^{2} + 1)}{2 p}$

Step 3.3

Multiply $2$ by $2$ .

$\frac{4 p^{2} - (4 p^{2} + 1)}{2 p}$

Step 3.4

Apply the distributive property.

$\frac{4 p^{2} - (4 p^{2}) - 1 \cdot 1}{2 p}$

Step 3.5

Multiply $4$ by $- 1$ .

$\frac{4 p^{2} - 4 p^{2} - 1 \cdot 1}{2 p}$

Step 3.6

Multiply $- 1$ by $1$ .

$\frac{4 p^{2} - 4 p^{2} - 1}{2 p}$

Step 3.7

Subtract $4 p^{2}$ from $4 p^{2}$ .

$\frac{0 - 1}{2 p}$

Step 3.8

Subtract $1$ from $0$ .

$\frac{- 1}{2 p}$

Step 4

Move the negative in front of the fraction.

$- \frac{1}{2 p}$