Simplify (2x^2+1)/2+(3x^2-5)/3

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

To write $\frac{2 x^{2} + 1}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

To write $\frac{3 x^{2} - 5}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{2 x^{2} + 1}{2}$ by $\frac{3}{3}$ .

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

Multiply $2$ by $3$ .

$\frac{(2 x^{2} + 1) \cdot 3}{6} + \frac{3 x^{2} - 5}{3} \cdot \frac{2}{2}$

Multiply $\frac{3 x^{2} - 5}{3}$ by $\frac{2}{2}$ .

$\frac{(2 x^{2} + 1) \cdot 3}{6} + \frac{(3 x^{2} - 5) \cdot 2}{3 \cdot 2}$

Multiply $3$ by $2$ .

$\frac{(2 x^{2} + 1) \cdot 3}{6} + \frac{(3 x^{2} - 5) \cdot 2}{6}$

Combine the numerators over the common denominator.

$\frac{(2 x^{2} + 1) \cdot 3 + (3 x^{2} - 5) \cdot 2}{6}$

Simplify the numerator.

Apply the distributive property.

$\frac{2 x^{2} \cdot 3 + 1 \cdot 3 + (3 x^{2} - 5) \cdot 2}{6}$

Multiply $3$ by $2$ .

$\frac{6 x^{2} + 1 \cdot 3 + (3 x^{2} - 5) \cdot 2}{6}$

Multiply $3$ by $1$ .

$\frac{6 x^{2} + 3 + (3 x^{2} - 5) \cdot 2}{6}$

Apply the distributive property.

$\frac{6 x^{2} + 3 + 3 x^{2} \cdot 2 - 5 \cdot 2}{6}$

Multiply $2$ by $3$ .

$\frac{6 x^{2} + 3 + 6 x^{2} - 5 \cdot 2}{6}$

Multiply $- 5$ by $2$ .

$\frac{6 x^{2} + 3 + 6 x^{2} - 10}{6}$

Add $6 x^{2}$ and $6 x^{2}$ .

$\frac{12 x^{2} + 3 - 10}{6}$

Subtract $10$ from $3$ .

$\frac{12 x^{2} - 7}{6}$