Question

Which of the following is the correct equation when expressed in terms of x, y, and z for the given expression?

A) (x + y) + (y + z) + (x + z) = 4
B) (x - y) + (y + z) + (x + z) = 4
C) (x / y) + (y / z) + (x / z) = 4
D) (x / (x + y)) + (y / (y + z)) + (x / (x + z)) = 4

Answer 1

None of the provided options (A, B, C, D) correctly equal to 4 when the given values of x=1, y=2, and z=3 are plugged in.

Step-by-step explanation:

The student is asking for the correct equation expressed in terms of x, y, and z for the given expressions. Let's evaluate each of the provided options with the given values of x, y, and z:

• For option A: (x + y) + (y + z) + (x + z), if we plug in x = 1, y = 2, and z = 3, we get (1+2)+(2+3)+(1+3) which equals to 12, not 4.
• For option B: (x - y) + (y + z) + (x + z), using the same values, we get (1-2)+(2+3)+(1+3) which equals to 7, not 4.
• For option C: (x / y) + (y / z) + (x / z), using the same values, we get (1/2)+(2/3)+(1/3) which does not equal to 4.
• For option D: (x / (x + y)) + (y / (y + z)) + (x / (x + z)), using the same values, we get (1/(1+2))+(2/(2+3))+(1/(1+3)) which equals to (1/3)+(2/5)+(1/4). This expression simplifies to 47/60, which also does not equal 4.

Therefore, none of the provided options correctly equal to 4 with the given x, y, and z values of 1, 2, and 3, respectively.