Algebra Examples

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

Step 1

Combine the numerators over the common denominator.

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

Step 2

Add $2 x^{2}$ and $2 x^{2}$ .

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

Step 3

Add $3$ and $1$ .

$\frac{4 x^{2} + 4}{x^{2} + 1}$

Step 4

Factor $4$ out of $4 x^{2} + 4$ .

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Step 4.1

Factor $4$ out of $4 x^{2}$ .

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

Step 4.2

Factor $4$ out of $4$ .

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

Step 4.3

Factor $4$ out of $4 (x^{2}) + 4 (1)$ .

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

Step 5

Cancel the common factor of $x^{2} + 1$ .

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Step 5.1

Cancel the common factor.

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

Step 5.2

Divide $4$ by $1$ .

$4$