Suppose that f(x) and g(x) are given by the power series

f(x) = 3 + 5 x + 2 x^2 + 4 x^3 + \cdots

and

g(x) = 15 + 37 x + 36 x^2 + 50 x^3 + \cdots .

By dividing power series, find the first few terms of the series for the quotient

h(x)=\displaystyle \frac{g(x)}{f(x)} = c_0+c_1 x +c_2 x^2 + c_3
x^3 + \cdots.

c_0 =

c_1 =

c_2 =

c_3 =

and

By dividing power series, find the first few terms of the series for the quotient

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