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

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

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

simplify

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

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

Solution steps

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

Join

\frac{1}{x ^{2}} - 3 : \frac{- 3 x ^{2} + 1}{x ^{2}}

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

Apply the fraction rule:

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

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

Factor

5 x^{3} - x : x (5 x^{2} - 1)

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

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

x^{2} = xx

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

Cancel the common factor:

x

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

\frac{( 33 x + 895 ) ^{2}}{42432196 ( 11 x ^{2} + 5 x + 6 )}

sin (π (1 - n))

10 (\frac{2}{5} - 2 x)

\frac{3}{4} (6 ln (6) + 5)

(p - 4) (12 - \frac{p}{2})

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