What is sqrt(1+((x-1)^2)/(4x)) ?

The solution to sqrt(1+((x-1)^2)/(4x)) is (x+1)/(2sqrt(x))

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simplify sqrt(1+((x-1)^2)/(4x))

simplify

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

\frac{x + 1}{2 x}

Solution steps

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

Join

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

= \frac{x ^{2} + 2 x + 1}{4 x}

Apply radical rule:

\frac{a}{b} = \frac{a}{b},

assuming

a \geq 0, b \geq 0

= \frac{x ^{2} + 2 x + 1}{4 x}

Simplify

x^{2} + 2 x + 1 : x + 1

= \frac{x + 1}{4 x}

Simplify

4 x : 2 x

= \frac{x + 1}{2 x}

y (3 y + 5)

- y^{0}

13 \times 13

(6 m^{2} a^{- 1})^{- 3}

w^{2} + 16 w + 64

What is sqrt(1+((x-1)^2)/(4x)) ?
The solution to sqrt(1+((x-1)^2)/(4x)) is (x+1)/(2sqrt(x))