Respuesta :

[tex]\bold{[ \ Answer \ ]}[/tex]

[tex]\boxed{\bold{\frac{x^3\left(6x^2+4x-1\right)}{2}}}[/tex]

[tex]\bold{[ \ Explanation \ ]}[/tex]

  • [tex]\bold{Divide: \ \left(18x^3\:+\:12x^2\:-\:3x\right)\:\div \:6x^2}[/tex]

[tex]\bold{-------------------}[/tex]

  • [tex]\bold{Rewrite}[/tex]

[tex]\bold{18x^3+12x^2-3x \ = \ x^2\frac{x\left(6x^2+4x-1\right)}{2}}[/tex]

  • [tex]\bold{Rewrite}[/tex]

[tex]\bold{x^2\frac{x\left(6x^2+4x-1\right)}{2}}[/tex]

  • [tex]\bold{Multiply \ Fractions \ (a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c})}[/tex]

[tex]\bold{\frac{x\left(6x^2+4x-1\right)x^2}{2}}[/tex]

  • [tex]\bold{Rewrite}[/tex]

[tex]\bold{x\left(6x^2+4x-1\right)x^2 \ = \ x^3\left(6x^2+4x-1\right)}[/tex]

  • [tex]\bold{Simplify}[/tex]

[tex]\bold{\frac{x^3\left(6x^2+4x-1\right)}{2}}[/tex]

[tex]\boxed{\bold{[] \ Eclipsed \ []}}[/tex]

carlosego

For this case, we must divide the following expression:

[tex]\frac {18x ^ 3 + 12x ^ 2-3x} {6x ^ 2} =[/tex]

We separate:

[tex]\frac {18x ^ 3} {6x ^ 2} + \frac {12x ^ 2} {6x ^ 2} - \frac {3x} {6x ^ 2} =[/tex]

By definition of power properties we have to:

[tex]\frac {a ^ m} {a ^ n} = a ^ {m-n}[/tex]

So:

[tex]3x ^ {3-2} + 2x^{2-2} - \frac {1} {2} x ^ {1-2} =\\3x ^ 1 + 2- \frac {1} {2} x ^ {- 1} =[/tex]

By definition of power properties we have to:

[tex]a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]

Then:

[tex]3x + 2- \frac {1} {2} * \frac {1} {x} =\\3x + 2- \frac {1} {2x}[/tex]

Answer:

[tex]3x + 2- \frac {1} {2x}[/tex]

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