Simplify (3x)/(2x+6)+(3-2x)/(2(x+3))

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

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

Factor $2$ out of $2 x$ .

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

Factor $2$ out of $6$ .

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

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

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

Combine the numerators over the common denominator.

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

Subtract $2 x$ from $3 x$ .

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

Cancel the common factor of $x + 3$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{1}{2}$

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{2}$

Decimal Form:

$0.5$