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

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

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

simplify

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

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

Solution steps

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

Apply Perfect Square Formula:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

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

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

Simplify

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

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

1 - (- 8)

(4 + ((2 - 5)^{2} - 4 (7 - 5)^{3} + 2 (\frac{15}{3}))) - 16

- 4 - - 25

4 \frac{3}{5} + 7 \frac{1}{2}

\frac{0}{x ^{2}}

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