What is maclaurin (4x)/(x^2+2x-3) ?

The answer to maclaurin (4x)/(x^2+2x-3) is -4/3 x-8/9 x^2-28/27 x^3-80/81 x^4-244/243 x^5+\ldots

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maclaurin (4x)/(x^2+2x-3)

maclaurin

\frac{4 x}{x ^{2} + 2 x - 3}

- \frac{4}{3} x - \frac{8}{9} x^{2} - \frac{28}{27} x^{3} - \frac{80}{81} x^{4} - \frac{244}{243} x^{5} + \dots

Solution steps

Apply the Maclaurin Formula

= 0 + \frac{\frac{d}{d x} ( \frac{4 x}{x ^{2} + 2 x - 3} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( \frac{4 x}{x ^{2} + 2 x - 3} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( \frac{4 x}{x ^{2} + 2 x - 3} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 0 + \frac{- \frac{4}{3}}{1 !} x + \frac{- \frac{16}{9}}{2 !} x^{2} + \frac{- \frac{56}{9}}{3 !} x^{3} + \frac{- \frac{640}{27}}{4 !} x^{4} + \frac{- \frac{9760}{81}}{5 !} x^{5} + \dots

Refine

= - \frac{4}{3} x - \frac{8}{9} x^{2} - \frac{28}{27} x^{3} - \frac{80}{81} x^{4} - \frac{244}{243} x^{5} + \dots

2 e^{(5 t - 2)}

\frac{d}{d x} (\frac{1}{5 - 11 e ^{x}})

\int \frac{2}{3} x^{\frac{1}{2}} d x

y^{2} = x^{3}, x = 1

\int \frac{x ^{3}}{e ^{x^{2}}} d x

What is maclaurin (4x)/(x^2+2x-3) ?
The answer to maclaurin (4x)/(x^2+2x-3) is -4/3 x-8/9 x^2-28/27 x^3-80/81 x^4-244/243 x^5+\ldots