The question says “Which of the following is equal to -1/2x - 1/4y + 1/xy + 1/8?”. It’s multiple choice but I do not understand how to go from (-4y-2x+8+xy)/8xy to the Answer choices. Looking for explanation of the process used to solve.

Is the answer C?

I used the following strategies-

choose numbers-

case 1-

plug in number x=1,y=1

equation simplifies to 3/8 .

use the same x=1,y=1 in answer choices…

you will be left with B and C options.

case 2-

now try a different case

x=1, y=2

equations simplifies to value 0.

plug it in B and C.

answer will be C.

Algebraic approach-

you need to make denominators equal in the equation given in question.

It’s like finding LCM - and the least common multiple diving all of the denominators in 8xy.

now multiply and divide each term with the remaining values … like

-1/2x => -1*(4y) /2x*(4y) => -4y/8xy.

do this for all the values and it should simpify to (xy-2x-4y+8) /8xy.

If you simplify numerator of option C it will be equal to above value .

Thank You so much! Especially with two strategies