SOLUTION: A pleasant day dear Sir / Madam, please help me with this word problem involving rational expressions. The denominator of a fraction is 5 less than the numerator. If t

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Question 683685: A pleasant day dear Sir / Madam,
please help me with this word problem involving rational expressions.
The denominator of a fraction is 5 less than the numerator. If the denominator is doubled and the numerator is decreased by 5, the sum of the original fraction and the new one is 4. Find the original fraction.
Thank you very much for your help!
Answer by MathTherapy(10858) About Me  (Show Source):
You can put this solution on YOUR website!

A pleasant day dear Sir / Madam,
please help me with this word problem involving rational expressions.
The denominator of a fraction is 5 less than the numerator. If the denominator is doubled and the numerator is decreased by 5, the sum of the original fraction and the new one is 4. Find the original fraction.
Thank you very much for your help!

Let numerator of original fraction be N
Then denominator is: N – 5
Doubling the denominator results in: 2(N – 5)
Decreasing the numerator by 5 results in: N – 5

Original fraction: N%2F%28N+-+5%29

Altered fraction: %28N+-+5%29%2F%282%28N+-+5%29%29

Therefore, N%2F%28N+-+5%29+%2B+%28N+-+5%29%2F%282%28N+-+5%29%29+=+4

2N + (N – 5) = 4(2)(N -5) ------ Multiplying by LCD, 2(N – 5)
2N + N – 5 = 8N – 40
3N – 8N = - 40 + 5
– 5N = - 35
N, or original numerator = %28-+35%29%2F-+5, or highlight%287%29

Original denominator = 7 - 5, or highlight%282%29

Original fraction: highlight_green%287%2F2%29

You can do the check!!

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