What is 1/(tsqrt(1+t))-1/t ?

The solution to 1/(tsqrt(1+t))-1/t is (1-sqrt(t+1))/(tsqrt(t+1))

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simplify 1/(tsqrt(1+t))-1/t

simplify

\frac{1}{t 1 + t} - \frac{1}{t}

\frac{1 - t + 1}{t t + 1}

Solution steps

\frac{1}{t 1 + t} - \frac{1}{t}

Least Common Multiplier of

t 1 + t, t : t t + 1

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

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

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

\frac{- 9}{- 2}

\frac{2}{5} \cdot 100

\frac{14 4 ^{14}}{14 4 ^{2}}

What is 1/(tsqrt(1+t))-1/t ?
The solution to 1/(tsqrt(1+t))-1/t is (1-sqrt(t+1))/(tsqrt(t+1))