What is (x^2-2x^1)/(2x^3)-(3x^2-3x^5)/(2x^3) ?

The solution to (x^2-2x^1)/(2x^3)-(3x^2-3x^5)/(2x^3) is (x-2)/(2x^2)+(3(x-1)(x^2+x+1))/(2x)

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simplify (x^2-2x^1)/(2x^3)-(3x^2-3x^5)/(2x^3)

simplify

\frac{x ^{2} - 2 x ^{1}}{2 x ^{3}} - \frac{3 x ^{2} - 3 x ^{5}}{2 x ^{3}}

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

Solution steps

\frac{x ^{2} - 2 x ^{1}}{2 x ^{3}} - \frac{3 x ^{2} - 3 x ^{5}}{2 x ^{3}}

Apply exponent rule:

a^{1} = a

x^{1} = x

= \frac{x ^{2} - 2 x}{2 x ^{3}} - \frac{3 x ^{2} - 3 x ^{5}}{2 x ^{3}}

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

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

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

Apply rule:

a - (- b) = a + b

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

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

lo g_{2} (28) + lo g_{2} (6) - lo g_{2} (21)

\frac{10 - 6 i}{6 + 5 i}

925

- 7 - (- 8)

- lo g_{10} (0.002)

What is (x^2-2x^1)/(2x^3)-(3x^2-3x^5)/(2x^3) ?
The solution to (x^2-2x^1)/(2x^3)-(3x^2-3x^5)/(2x^3) is (x-2)/(2x^2)+(3(x-1)(x^2+x+1))/(2x)