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

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

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

expand

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

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

Solution steps

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

Expand

2 e^{x^{2}} (x^{2} - 1) : 2 e^{x^{2}} x^{2} - 2 e^{x^{2}}

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

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

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

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

Cancel

\frac{2 e ^{x^{2}} x ^{2}}{x ^{3}} : \frac{2 e ^{x^{2}}}{x}

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

(5 x^{\frac{1}{2}} + 3) (5 x^{\frac{1}{2}} - 3)

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

sin (x) (tan (x) + csc (x))

+ (x + x y) d y

s im pl i y (3 x + 4 y) + 5 x + 8 x + 4 y

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