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

The solution to expand (x^2-1)e^{1/(x-3)} is e^{1/(x-3)}x^2-e^{1/(x-3)}

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expand (x^2-1)e^{1/(x-3)}

expand

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

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

Solution steps

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

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

Apply the distributive law:

a (b - c) = ab - a c

a = e^{\frac{1}{x - 3}}, b = x^{2}, c = 1

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

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

Multiply:

1 \cdot e^{\frac{1}{x - 3}} = e^{\frac{1}{x - 3}}

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

- \frac{e ^{x}}{( c + e ^{x} ) ^{2}}

, (5 x - 8 q^{2}) (2 (m - 2))

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

\frac{4 x ^{2} - 8 x + 1}{( x + 2 ) ( x ^{2} - 2 x + 3 )}

π (2 ln (3) + \frac{2}{3})

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