Are the numbers after the letters meant to be subscripts, superscripts, or something else? Assuming the second, you have:
. . . . .(p<sup>5</sup>x + 2y) / (p<sup>2</sup>x + 4y)
Looking at the leading terms and thinking about how long division works, there is only one possible correct answer (other than "none of these"). To check that answer, multiply it against the denominator, and see if you get the numerator. If the multiplication checks out, then that answer is the correct solution for the division.
(This is similar to verifying that the correct answer to "12 / 4" is "3" by multiplying the 3 and the 4, and seeing that you do indeed get 12 for an answer.)
Eliz.