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**+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