What is join ae^v+b/v+c/(v^2) ?

The solution to join ae^v+b/v+c/(v^2) is (e^vav^2+vb+c)/(v^2)

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join ae^v+b/v+c/(v^2)

join

a e^{v} + \frac{b}{v} + \frac{c}{v ^{2}}

\frac{e ^{v} a v ^{2} + v b + c}{v ^{2}}

Solution steps

a e^{v} + \frac{b}{v} + \frac{c}{v ^{2}}

Convert element to fraction:

e^{v} a = \frac{e ^{v} a}{1}

= \frac{a e ^{v}}{1} + \frac{b}{v} + \frac{c}{v ^{2}}

Least Common Multiplier of

1, v, v^{2} : v^{2}

Adjust Fractions based on the LCM

= \frac{a e ^{v} v ^{2}}{v ^{2}} + \frac{b v}{v ^{2}} + \frac{c}{v ^{2}}

Since the denominators are equal, combine the fractions:

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

= \frac{a e ^{v} v ^{2} + b v + c}{v ^{2}}

\frac{x}{6 x + 4}

\frac{d}{d x} (3 csc (x) + \frac{5}{x})

x \to 0 lim (cos (x) x)

\frac{d y}{d x} = 4 y + 3 e^{8 x} (x + 1), y (0) = 1

\int (1 - 2 x)^{2} d x

What is join ae^v+b/v+c/(v^2) ?
The solution to join ae^v+b/v+c/(v^2) is (e^vav^2+vb+c)/(v^2)