Simplify ((1-x)/((2x-x^2)^(1/2)))^2

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

Step 1

Apply the product rule to $\frac{1 - x}{{(2 x - x^{2})}^{\frac{1}{2}}}$ .

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

Step 2

Simplify the denominator.

Multiply the exponents in ${({(2 x - x^{2})}^{\frac{1}{2}})}^{2}$ .

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Factor $x$ out of $2 x - x^{2}$ .

Factor $x$ out of $2 x$ .

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

Factor $x$ out of $- x^{2}$ .

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

Factor $x$ out of $x \cdot 2 + x (- x)$ .

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