Algebra Examples

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

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.

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Step 2.1

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

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Step 2.1.1

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

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

Step 2.1.2

Cancel the common factor of $2$ .

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Step 2.1.2.1

Cancel the common factor.

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

Step 2.1.2.2

Rewrite the expression.

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

Step 2.2

Simplify.

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

Step 2.3

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

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Step 2.3.1

Factor $x$ out of $2 x$ .

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

Step 2.3.2

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

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

Step 2.3.3

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

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