Question

I don't understand what the answer is supposed to be, none of my answers match.

Answer 1

The rational expression is the following

$\frac{\frac{x-1}{6xy}}{\frac{5}{2y}}$

By applying the sandwich rule:

we have

$\frac{\frac{x-1}{6xy}}{\frac{5}{2y}}=\frac{(x-1)(2y)}{(6xy)(5)}$

which gives

$\frac{\frac{x-1}{6xy}}{\frac{5}{2y}}=\frac{(x-1)(2y)}{(6xy)(5)}=\frac{(x-1)(2y)}{(2\cdot3xy)(5)}=\frac{(x-1)(2y)}{(3x\cdot2y)(5)}=\frac{x-1}{3x\cdot5}=\frac{x-1}{15x}$

then, the answer is option 2.