If x ,y and z are positive numbers and x-y=z, then which of the following must equal 2?A) (x-y)/2z B) (x+y)/(z+2y) C)(2y+2z)/(x+y)...

We'll replace the result of the difference x - y by z, at
the numerator of the 1st option.

(x-y)/2z =
z/2z

We'll simplify and we'll
get:

(x-y)/2z = 1/2

Since the
result is not equal 2, we'll reject the A) option.

We'll
check in B)
option.

(x+y)/(z+2y)

We'll
replace z by x - y:

(x+y)/(z+2y) = (x+y)/(x - y +
2y)

(x+y)/(z+2y) = (x+y)/(x+y) =
1

Since the result is not equal 2, we'll reject the B)
option.

We'll check in C)
option.

(2y+2z)/(x+y)

We'll
factorize the numerator by
2:

2(y+z)/(x+y)

But y + z = x
=> 2(y+z)/(x+y) = 2x/(x+y)

Since the result is not
equal 2, we'll reject the C) option.

We'll check in D)
option.

(2x+y)/(z+y) = (2z + 2y + y)/(z+y) =
(2z+3y)/(z+y)

Since the result is not equal 2, we'll reject
the D) option.

We'll check in E)
option.

2x/(z+y)

We'll replace
z + y by x:

2x/(z+y) = 2x/x =
2

Since the result is equal 2, we'll accept
the E) option as the correct one.