Simplify ( square root of x+1)÷( square root of 4-x)

$\sqrt{x + 1} \div \sqrt{4 - x}$

Rewrite the division as a fraction.

$\frac{\sqrt{x + 1}}{\sqrt{4 - x}}$

Multiply $\frac{\sqrt{x + 1}}{\sqrt{4 - x}}$ by $\frac{\sqrt{4 - x}}{\sqrt{4 - x}}$ .

$\frac{\sqrt{x + 1}}{\sqrt{4 - x}} \cdot \frac{\sqrt{4 - x}}{\sqrt{4 - x}}$

Combine and simplify the denominator.

Multiply $\frac{\sqrt{x + 1}}{\sqrt{4 - x}}$ by $\frac{\sqrt{4 - x}}{\sqrt{4 - x}}$ .

$\frac{\sqrt{x + 1} \sqrt{4 - x}}{\sqrt{4 - x} \sqrt{4 - x}}$

Raise $\sqrt{4 - x}$ to the power of $1$ .

$\frac{\sqrt{x + 1} \sqrt{4 - x}}{{\sqrt{4 - x}}^{1} \sqrt{4 - x}}$

Raise $\sqrt{4 - x}$ to the power of $1$ .

$\frac{\sqrt{x + 1} \sqrt{4 - x}}{{\sqrt{4 - x}}^{1} {\sqrt{4 - x}}^{1}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{\sqrt{x + 1} \sqrt{4 - x}}{{\sqrt{4 - x}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{\sqrt{x + 1} \sqrt{4 - x}}{{\sqrt{4 - x}}^{2}}$

Rewrite ${\sqrt{4 - x}}^{2}$ as $4 - x$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{4 - x}$ as ${(4 - x)}^{\frac{1}{2}}$ .

$\frac{\sqrt{x + 1} \sqrt{4 - x}}{{({(4 - x)}^{\frac{1}{2}})}^{2}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{\sqrt{x + 1} \sqrt{4 - x}}{{(4 - x)}^{\frac{1}{2} \cdot 2}}$

Combine $\frac{1}{2}$ and $2$ .

$\frac{\sqrt{x + 1} \sqrt{4 - x}}{{(4 - x)}^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{\sqrt{x + 1} \sqrt{4 - x}}{{(4 - x)}^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{\sqrt{x + 1} \sqrt{4 - x}}{{(4 - x)}^{1}}$

Simplify.

$\frac{\sqrt{x + 1} \sqrt{4 - x}}{4 - x}$

Combine using the product rule for radicals.

$\frac{\sqrt{(x + 1) (4 - x)}}{4 - x}$