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# The denominator of a fraction in simplest form is greater than the numerator by 3. If 7 is added to the numerator, and 5 added to the denominator, then the

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The denominator of a fraction in simplest form is greater than the numerator by 3. If 7 is added to the numerator, and 5 added to the denominator, then the fraction itself is increased by

1/2

. Find the original fraction.

Guest Mar 10, 2017
#1
+87334
+5

Let the original fraction = n / [n + 3]

And we have that

[n + 7] / [n + 8]  =  n / [n + 3]  + 1/2

[ n + 7] / [n + 8]  =  [ 2n + n + 3] / [ 2(n + 3) ]   cross-multiply

[2(n +3)] [ n + 7]= [2n + n + 3] [ n + 8]

[2(n +3)] [ n + 7]= [3n + 3] [ n + 8]

2 [ n + 3] [ n + 7 ] = 3 [n + 1] [ n + 8 ]

2 [ n ^2 + 10n + 21] = 3 [ n^2 + 9n + 8]

2n^2 + 20n + 42  =  3n^2 + 27n + 24

n ^2 + 7n - 18  = 0       factor

(n + 9) ( n - 2)   = 0      and n  = -9 or n = 2

So....one possibility...when n = 2

9 / 10  = 2/5 + 1/2

9/10  = 9/10

Or  when  n = -9

-2/-1  = -9/-6 + 1/2

2  =  3/2 + 1/2

2 = 2

So....the original fractions were   2/5   or 3/2

CPhill  Mar 10, 2017