Simplify (3+1/2)/(3-1/2)

$\frac{3 + \frac{1}{2}}{3 - \frac{1}{2}}$

Multiply the numerator and denominator of the complex fraction by $2$ .

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

$\frac{2}{2} \cdot \frac{3 + \frac{1}{2}}{3 - \frac{1}{2}}$

Combine.

$\frac{2 (3 + \frac{1}{2})}{2 (3 - \frac{1}{2})}$

Apply the distributive property.

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

Simplify by cancelling.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{1}{2}$ into the numerator.

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{2 \cdot 3 + 1}{2 \cdot 3 - 1}$

Simplify the numerator.

Multiply $2$ by $3$ .

$\frac{6 + 1}{2 \cdot 3 - 1}$

Add $6$ and $1$ .

$\frac{7}{2 \cdot 3 - 1}$

Simplify the denominator.

Multiply $2$ by $3$ .

$\frac{7}{6 - 1}$

Subtract $1$ from $6$ .

$\frac{7}{5}$

The result can be shown in multiple forms.

Exact Form:

$\frac{7}{5}$

Decimal Form:

$1.4$

Mixed Number Form:

$1 \frac{2}{5}$