What is 1/(xsqrt(1+x))-1/x ?

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

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simplify 1/(xsqrt(1+x))-1/x

simplify

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

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

Solution steps

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

Least Common Multiplier of

x 1 + x, x : x x + 1

Adjust Fractions based on the LCM

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

Apply the fraction rule:

\frac{a}{c} - \frac{b}{c} = \frac{a - b}{c}

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

2 (3 x + 7)

\frac{6 x ^{2}}{x ( x - 5 )} \cdot \frac{x - 5}{8 ( x + 3 )}

(2 x - 1) 2

lo g_{2} (8192)

\frac{8 x ^{3} - 27 y ^{3}}{2 x - 3 y}

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