Answer :
Answer:
(x + y)/x is greater than x/(x + y)
Step-by-step explanation:
Given.
x > y
y > 0
Required
Which is greater?
x/(x + y) or (x + y)/x
Since x is greater than y & y > 0
Then definitely,
x + y > x
By the above analysis:
(x + y)/x is an improper fraction because the numerator (x + y) is greater than the denominator (x)
While
x/(x + y) is a proper fraction because the numerator (x) is lesser than the denominator.
All improper fractions are greater than all proper fractions,
Hence:
(x + y)/x is greater than x/(x + y)
To further explain this:
Take
x = 3 and y = 2
x/(x + y) = 3/(3 + 2) = 3/5 = 0.6
(x + y)/x = (3 + 2)/3 = 5/3 = 1.67
See that (x + y)/x is greater than x/(x + y)
And this is so for all values of x and y
Where x > y and y > 0