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

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

Step 1

Combine the numerators over the common denominator.

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

Step 2

Add $3 x$ and $x$ .

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

Step 3

Add $- 5$ and $3$ .

$\frac{4 x - 2}{2}$

Step 4

Cancel the common factor of $4 x - 2$ and $2$ .

Factor $2$ out of $4 x$ .

$\frac{2 (2 x) - 2}{2}$

Factor $2$ out of $- 2$ .

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

Factor $2$ out of $2 (2 x) + 2 (- 1)$ .

$\frac{2 (2 x - 1)}{2}$

Cancel the common factors.

Factor $2$ out of $2$ .

$\frac{2 (2 x - 1)}{2 (1)}$

Cancel the common factor.

$\frac{2 (2 x - 1)}{2 \cdot 1}$

Rewrite the expression.

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

Divide $2 x - 1$ by $1$ .

$2 x - 1$