What is 1/((2sqrt(x)))-1/((2^{3/2))} ?

The solution to 1/((2sqrt(x)))-1/((2^{3/2))} is (2^{1/2}-x^{1/2})/(2*2^{1/2)x^{1/2}}

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simplify 1/((2sqrt(x)))-1/((2^{3/2))}

simplify

\frac{1}{( 2 x )} - \frac{1}{( 2 ^{\frac{3}{2}} )}

\frac{2 ^{\frac{1}{2}} - x ^{\frac{1}{2}}}{2 \cdot 2 ^{\frac{1}{2}} x ^{\frac{1}{2}}}

Solution steps

\frac{1}{2 x} - \frac{1}{2 ^{\frac{3}{2}}}

Least Common Multiplier of

2 x, 2^{\frac{3}{2}} : 2^{1 + \frac{3}{2}} x^{\frac{1}{2}}

Adjust Fractions based on the LCM

= \frac{2 \cdot 2 ^{\frac{1}{2}}}{2 ^{1 + \frac{3}{2}} x ^{\frac{1}{2}}} - \frac{2 x ^{\frac{1}{2}}}{2 ^{1 + \frac{3}{2}} x ^{\frac{1}{2}}}

Apply the fraction rule:

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

= \frac{2 \cdot 2 ^{\frac{1}{2}} - 2 x ^{\frac{1}{2}}}{2 ^{1 + \frac{3}{2}} x ^{\frac{1}{2}}}

Cancel

\frac{2 \cdot 2 ^{\frac{1}{2}} - 2 x ^{\frac{1}{2}}}{2 ^{1 + \frac{3}{2}} x ^{\frac{1}{2}}} : \frac{2 ^{\frac{1}{2}} - x ^{\frac{1}{2}}}{2 \cdot 2 ^{\frac{1}{2}} x ^{\frac{1}{2}}}

= \frac{2 ^{\frac{1}{2}} - x ^{\frac{1}{2}}}{2 \cdot 2 ^{\frac{1}{2}} x ^{\frac{1}{2}}}

a (a + 1) (a + 2) (a + 3) - 15

3 \frac{x ^{2}}{x} + \frac{2}{6} \frac{x ^{4}}{( x ^{2} + 5 x + 6 )}

x^{4} - 17 x^{2} y^{2} - 84 y^{4}

\frac{( 24 z ^{2} - 12 z + 6 )}{( - 6 )}

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What is 1/((2sqrt(x)))-1/((2^{3/2))} ?
The solution to 1/((2sqrt(x)))-1/((2^{3/2))} is (2^{1/2}-x^{1/2})/(2*2^{1/2)x^{1/2}}