If X does not = Y, but X/Y + X = Y/X + X, what does 1/X + 1/Y equal?
X/Y + X/1 = Y/X + X/1
X/1 cancels out
X/Y = Y/X
X^2 = Y^2
+/-X = +/-Y
In effect, if X != Y, then:
X = -Y or -X = Y
So,
1/X + 1/Y = 0
sorrry, but I made a typo.
x/y + x = Y/x + Y.
No problem! Let's start from the equation you provided:
X/Y + X = Y/X + Y
To find the value of 1/X + 1/Y, we need to rewrite the given equation in terms of 1/X and 1/Y.
To do that, we'll start by multiplying both sides of the equation by (1/X)(1/Y):
(1/X)(X/Y + X) = (1/X)(Y/X + Y)
Simplifying the left side:
(X/Y) * (1/X) + (X) * (1/X) = (Y/X) * (1/Y) + (Y) * (1/Y)
1/Y + 1 = 1/X + 1/Y
Now, we have the equation in terms of 1/X and 1/Y. So, 1/X + 1/Y is equal to 1/Y + 1.
Therefore, 1/X + 1/Y is equal to 1/Y + 1.