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 .
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Thank You so much! Especially with two strategies
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