What is (1/2)/(x/a)a^2+2a^3-4a^4 ?

The solution to (1/2)/(x/a)a^2+2a^3-4a^4 is (a^3)/(2x)+2a^3-4a^4

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simplify (1/2)/(x/a)a^2+2a^3-4a^4

simplify

\frac{\frac{1}{2}}{\frac{x}{a}} a^{2} + 2 a^{3} - 4 a^{4}

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

Solution steps

\frac{\frac{1}{2}}{\frac{x}{a}} a^{2} + 2 a^{3} - 4 a^{4}

Simplify

\frac{\frac{1}{2}}{\frac{x}{a}} : \frac{a}{2 x}

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

Apply the fraction rule:

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

\frac{a}{2 x} a^{2} = \frac{a a ^{2}}{2 x}

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

Simplify

a a^{2} : a^{3}

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

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

(a^{2} + 1)^{3}

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

3 x^{2} + 2 x^{3} + 8 x - 5 x y

(- 3 a^{2} b^{2}) (4 a^{5} b^{3})^{3}

What is (1/2)/(x/a)a^2+2a^3-4a^4 ?
The solution to (1/2)/(x/a)a^2+2a^3-4a^4 is (a^3)/(2x)+2a^3-4a^4