Answer:
The quotient is:
[tex]xy^6+2y-6[/tex]
Step-by-step explanation:
We are asked to find the quotient of the mathematical expression which is given in terms of variable x and y is represented as:
[tex]=\dfrac{6x^2y^8+12xy^3-36xy^2}{6xy^2}[/tex]
Here the numerator is:
[tex]6x^2y^8+12xy^3-36xy^2[/tex]
and the denominator is:
[tex]6xy^2[/tex]
We can also represent our numerator term by the method of factoring it as:
[tex]6x^2y^8+12xy^3-36xy^2=6xy^2(xy^6+2y-6)[/tex]
Hence, our expression gets converted by replacing the numerator term to:
[tex]\dfrac{6x^2y^8+12xy^3-36xy^2}{6xy^2}=\dfrac{6xy^2(xy^6+2y-6)}{6xy^2}\\\\\dfrac{6x^2y^8+12xy^3-36xy^2}{6xy^2}=xy^6+2y-6[/tex]
Hence, the quotient is:
[tex]xy^6+2y-6[/tex]
