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1. Find the coefficient of x^3in(√(x^5 )+3/√(x^3))^6

${(\frac{\sqrt{x^{5}} + 3}{\sqrt{x^{3}}})^{6} = (\frac{x^{\frac{5}{2}} + 3}{x^{\frac{3}{2}}})}^{6} = (x + 3 x^{- \frac{3}{2}})^{6} T_{r} =^{6} C_{r} x^{r} (3 x^{- \frac{3}{2}})^{6 - r} =^{6} C_{r} 3^{6 - r} x^{r + \frac{3}{2} (r - 6)} =^{6} C_{r} 3^{6 - r} x^{\frac{5 r}{2} - 9} x^{\frac{5 r}{2} - 9} = x^{3} \frac{5 r}{2} - 9 = 3 T h i s d o e s n o t g i v e a v a l u e o f r, t h a t i s a n a t u r a l n u m b e r . P l e a s e c h e c k y o u r q u e s t i o n$

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