What is sqrt(2x-x^2)sqrt(1+((1-x)^2)/(2x-x^2)) ?

The solution to sqrt(2x-x^2)sqrt(1+((1-x)^2)/(2x-x^2)) is 1

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simplify sqrt(2x-x^2)sqrt(1+((1-x)^2)/(2x-x^2))

simplify

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

1

Solution steps

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

Apply radical rule:

a b = a \cdot b

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

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

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

= 1

Apply rule

1 = 1

= 1

(3 x - 2)^{3} \cdot (3 y - 2)^{3}

0.693 (220 + 2 (10000)) (10 \cdot 1 0^{- 6})

e^{- 7.7}

(\frac{1 + x}{1 - x})

(e^{5 x})^{^{'}}

What is sqrt(2x-x^2)sqrt(1+((1-x)^2)/(2x-x^2)) ?
The solution to sqrt(2x-x^2)sqrt(1+((1-x)^2)/(2x-x^2)) is 1