What is expand y(x^2+1)coth(x/3) ?

The solution to expand y(x^2+1)coth(x/3) is ycoth(x/3)x^2+ycoth(x/3)

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expand y(x^2+1)coth(x/3)

expand

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

y coth (\frac{x}{3}) x^{2} + y coth (\frac{x}{3})

Solution steps

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

= y coth (\frac{x}{3}) (x^{2} + 1)

Apply the distributive law:

a (b + c) = ab + a c

y coth (\frac{x}{3}) (x^{2} + 1) = y coth (\frac{x}{3}) x^{2} + y coth (\frac{x}{3}) \cdot 1

= y coth (\frac{x}{3}) x^{2} + y coth (\frac{x}{3}) \cdot 1

Apply rule:

a \cdot 1 = a

y coth (\frac{x}{3}) \cdot 1 = y coth (\frac{x}{3})

= y coth (\frac{x}{3}) x^{2} + y coth (\frac{x}{3})

\frac{- 5 t + 21}{( t + 1 ) ^{3}}

32 (4 + 23)

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

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

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

What is expand y(x^2+1)coth(x/3) ?
The solution to expand y(x^2+1)coth(x/3) is ycoth(x/3)x^2+ycoth(x/3)