Simplify (x^2+2)/4+(2x^2-1)/5

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

To write $\frac{x^{2} + 2}{4}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

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

To write $\frac{2 x^{2} - 1}{5}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

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

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{x^{2} + 2}{4}$ by $\frac{5}{5}$ .

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

Multiply $4$ by $5$ .

$\frac{(x^{2} + 2) \cdot 5}{20} + \frac{2 x^{2} - 1}{5} \cdot \frac{4}{4}$

Multiply $\frac{2 x^{2} - 1}{5}$ by $\frac{4}{4}$ .

$\frac{(x^{2} + 2) \cdot 5}{20} + \frac{(2 x^{2} - 1) \cdot 4}{5 \cdot 4}$

Multiply $5$ by $4$ .

$\frac{(x^{2} + 2) \cdot 5}{20} + \frac{(2 x^{2} - 1) \cdot 4}{20}$

Combine the numerators over the common denominator.

$\frac{(x^{2} + 2) \cdot 5 + (2 x^{2} - 1) \cdot 4}{20}$

Simplify the numerator.

Apply the distributive property.

$\frac{x^{2} \cdot 5 + 2 \cdot 5 + (2 x^{2} - 1) \cdot 4}{20}$

Move $5$ to the left of $x^{2}$ .

$\frac{5 \cdot x^{2} + 2 \cdot 5 + (2 x^{2} - 1) \cdot 4}{20}$

Multiply $2$ by $5$ .

$\frac{5 \cdot x^{2} + 10 + (2 x^{2} - 1) \cdot 4}{20}$

Apply the distributive property.

$\frac{5 x^{2} + 10 + 2 x^{2} \cdot 4 - 1 \cdot 4}{20}$

Multiply $4$ by $2$ .

$\frac{5 x^{2} + 10 + 8 x^{2} - 1 \cdot 4}{20}$

Multiply $- 1$ by $4$ .

$\frac{5 x^{2} + 10 + 8 x^{2} - 4}{20}$

Add $5 x^{2}$ and $8 x^{2}$ .

$\frac{13 x^{2} + 10 - 4}{20}$

Subtract $4$ from $10$ .

$\frac{13 x^{2} + 6}{20}$