Simplify ( square root of 9-x^2)÷( square root of 3+x)

$\sqrt{9 - x^{2}} \div \sqrt{3 + x}$

Rewrite the division as a fraction.

$\frac{\sqrt{9 - x^{2}}}{\sqrt{3 + x}}$

Simplify the numerator.

Rewrite $9$ as $3^{2}$ .

$\frac{\sqrt{3^{2} - x^{2}}}{\sqrt{3 + x}}$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 3$ and $b = x$ .

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

Combine $\sqrt{(3 + x) (3 - x)}$ and $\sqrt{3 + x}$ into a single radical.

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

Reduce the expression by cancelling the common factors.

Reduce the expression $\frac{(3 + x) (3 - x)}{3 + x}$ by cancelling the common factors.

Cancel the common factor.

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

Rewrite the expression.

$\sqrt{\frac{3 - x}{1}}$

Divide $3 - x$ by $1$ .

$\sqrt{3 - x}$