Simplify (x^2+6)/( square root of 1-x)

$\frac{x^{2} + 6}{\sqrt{1 - x}}$

Multiply $\frac{x^{2} + 6}{\sqrt{1 - x}}$ by $\frac{\sqrt{1 - x}}{\sqrt{1 - x}}$ .

$\frac{x^{2} + 6}{\sqrt{1 - x}} \cdot \frac{\sqrt{1 - x}}{\sqrt{1 - x}}$

Combine and simplify the denominator.

Multiply $\frac{x^{2} + 6}{\sqrt{1 - x}}$ by $\frac{\sqrt{1 - x}}{\sqrt{1 - x}}$ .

$\frac{(x^{2} + 6) \sqrt{1 - x}}{\sqrt{1 - x} \sqrt{1 - x}}$

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

$\frac{(x^{2} + 6) \sqrt{1 - x}}{{\sqrt{1 - x}}^{1} \sqrt{1 - x}}$

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

$\frac{(x^{2} + 6) \sqrt{1 - x}}{{\sqrt{1 - x}}^{1} {\sqrt{1 - x}}^{1}}$

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

$\frac{(x^{2} + 6) \sqrt{1 - x}}{{\sqrt{1 - x}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{(x^{2} + 6) \sqrt{1 - x}}{{\sqrt{1 - x}}^{2}}$

Rewrite ${\sqrt{1 - x}}^{2}$ as $1 - x$ .

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

$\frac{(x^{2} + 6) \sqrt{1 - x}}{{({(1 - x)}^{\frac{1}{2}})}^{2}}$

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

$\frac{(x^{2} + 6) \sqrt{1 - x}}{{(1 - x)}^{\frac{1}{2} \cdot 2}}$

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

$\frac{(x^{2} + 6) \sqrt{1 - x}}{{(1 - x)}^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{(x^{2} + 6) \sqrt{1 - x}}{{(1 - x)}^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{(x^{2} + 6) \sqrt{1 - x}}{{(1 - x)}^{1}}$

Simplify.

$\frac{(x^{2} + 6) \sqrt{1 - x}}{1 - x}$

Reorder factors in $\frac{(x^{2} + 6) \sqrt{1 - x}}{1 - x}$ .

$\frac{\sqrt{1 - x} (x^{2} + 6)}{1 - x}$