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)

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

E) 2x/(z+y)

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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.**

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