What is 1/2*(1/s+s/((s^2+36))) ?

The solution to 1/2*(1/s+s/((s^2+36))) is (s^2+18)/(s(s^2+36))

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simplify 1/2*(1/s+s/((s^2+36)))

simplify

\frac{1}{2} \cdot (\frac{1}{s} + \frac{s}{( s ^{2} + 36 )})

\frac{s ^{2} + 18}{s ( s ^{2} + 36 )}

Solution steps

\frac{1}{2} (\frac{1}{s} + \frac{s}{s ^{2} + 36})

Join

\frac{1}{s} + \frac{s}{s ^{2} + 36} : \frac{2 s ^{2} + 36}{s ( s ^{2} + 36 )}

= \frac{1}{2} \cdot \frac{2 s ^{2} + 36}{s ( s ^{2} + 36 )}

Apply the fraction rule:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{1 \cdot ( 2 s ^{2} + 36 )}{2 s ( s ^{2} + 36 )}

Apply rule:

1 \cdot a = a

1 \cdot (2 s^{2} + 36) = (2 s^{2} + 36)

= \frac{2 s ^{2} + 36}{2 s ( s ^{2} + 36 )}

Factor

2 s^{2} + 36 : 2 (s^{2} + 18)

= \frac{2 ( s ^{2} + 18 )}{2 s ( s ^{2} + 36 )}

Cancel the common factor:

2

= \frac{s ^{2} + 18}{s ( s ^{2} + 36 )}

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b^{3} - 8 c^{3}

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

\frac{( 9 + 12 a + 4 a ^{2} )}{( b ^{2} )}

What is 1/2*(1/s+s/((s^2+36))) ?
The solution to 1/2*(1/s+s/((s^2+36))) is (s^2+18)/(s(s^2+36))