Respuesta :

[tex]\bf \cfrac{\qquad \frac{6}{10x^2}\qquad }{\frac{6}{10x^3-60x^2}}\implies \cfrac{\underline{6}}{10x^2}\cdot \cfrac{10x^3-60x^2}{\underline{6}}\implies \cfrac{10x^3-60x^2}{10x^2} \\\\\\ \cfrac{\underline{10x^2}(x-6)}{\underline{10x^2}}\implies x-6[/tex]

Answer:  The correct option is (B) x - 6.

Step-by-step explanation:  We are given to simplify the following division :

[tex]\dfrac{6}{10x^2}~~~\textup{by}~~~\dfrac{6}{10x^3-60x^2}.[/tex]

The simplification of the above division is as follows :

[tex]\dfrac{6}{10x^2}~~~\textup{by}~~~\dfrac{6}{10x^3-60x^2}\\\\\\=\dfrac{\frac{6}{10x^2}}{\frac{6}{10x^3-60x^2}}\\\\\\=\dfrac{6}{10x^2}\times\dfrac{10x^3-60x^2}{6}\\\\\\=\dfrac{10x^3-60x^2}{10x^2}\\\\\\=\dfrac{10x^2(x-6)}{10x^2}\\\\=x-6.[/tex]

Thus, the required simplified form is (x - 6).

Option (B) is CORRECT.

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