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Silviax
Please merge if the topic already exists. I couldn't find it. Thank you.

If \(\frac{4}{5-a/b}=1\) which of the following must be true?

(A) a= 0
(B) b= 0
(C) a=1
(D) b=1
(E) a=b

Chetan2u has done a great job applying what I call the Something Method.

Given: \(\frac{4}{5-a/b}=1\)
So, we have: 4/something = 1
This means that something = 4
In other words, 5 - a/b = 4

Now we have 5 - a/b = 4
If 5 - something = 4, then something = 1
In other words, a/b = 1
If a/b = 1, then we can be certain that a = b

Answer:
Here's a video on the Something Method:
Something Method
[youtube]https://www.youtube.com/watch?v=mmTisgtNfTI[/youtube]
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Silviax
Please merge if the topic already exists. I couldn't find it. Thank you.

If \(\frac{4}{5-a/b}=1\) which of the following must be true?

(A) a= 0
(B) b= 0
(C) a=1
(D) b=1
(E) a=b
\(\frac{4}{5-a/b}=1\)

Or, \(4 = 5 - \frac{a}{b}\)

So, \(\frac{a}{b} = 1\)

Thus, \(a = b\) , Answer must be (E)
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\(\frac{4}{5 - \frac{a}{b}} = 1\)

=> 4 = 5 - \(\frac{a}{b}\)
=> \(\frac{a}{b}\) = 5 - 4 = 1

Since b is in the denominator
=> b ≠ 0

\(\frac{a}{b}\) = 1
=> a = b will always be true

So, Answer will be E
Hope it helps!
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To solve this question,
4/5-a/b I first found out what 5-a/b is
It’s is = to 5b-a/b
Let’s substitute it
4/5b-a/b = 4b/5b-a = 1
Now,what we need to know is that if a fraction is = 1 then both the numerator and denominator are the same
Let’s make an equation

4b = 5b-a
Add a from both sides
4b+a = 5b
Subtract 4b from each side
a=b


Answer = E

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