Algebra Examples

$\frac{4 x + 1}{x^{2} + 3} - \frac{2 x - 5}{x^{2} + 3}$

Step 1

Combine the numerators over the common denominator.

$\frac{4 x + 1 - (2 x - 5)}{x^{2} + 3}$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$\frac{4 x + 1 - (2 x) - - 5}{x^{2} + 3}$

Step 2.2

Multiply $2$ by $- 1$ .

$\frac{4 x + 1 - 2 x - - 5}{x^{2} + 3}$

Step 2.3

Multiply $- 1$ by $- 5$ .

$\frac{4 x + 1 - 2 x + 5}{x^{2} + 3}$

Step 3

Simplify terms.

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Step 3.1

Subtract $2 x$ from $4 x$ .

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

Step 3.2

Add $1$ and $5$ .

$\frac{2 x + 6}{x^{2} + 3}$

Step 3.3

Factor $2$ out of $2 x + 6$ .

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Step 3.3.1

Factor $2$ out of $2 x$ .

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

Step 3.3.2

Factor $2$ out of $6$ .

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

Step 3.3.3

Factor $2$ out of $2 x + 2 \cdot 3$ .

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