The denominator of a fraction is greater than the numerator by 1. If the fraction is increased by 1/12 if 2 is added to both the numerator and the denominator. What is the fraction?
+128732 x / [ x + 1 ] + 1/12 = [x + 2] / [ x + 1 + 2 ] simplify
x / [ x + 1 ] + 1/12 = [x + 2] /[ x + 3] simplify the left side
[ 12x + x + 1 ] / [ 12 (x + 1)] = [ x + 2] / [ x + 3]
[ 13x + 1 ] / [ 12x + 12] = [ x + 2] / [x + 3] cross-multiply
[ 13x + 1] [ x + 3 ] = [ 12x + 12 ] [ x + 2 ] simplify
13x^2 + 40x + 3 = 12x^2 + 36x + 24
x^2 + 4x - 21 = 0 factor
(x + 7) (x - 3) = 0 x = - 7 or x = 3
Check -7
-7 / [ -7 + 1 ] + 1/12 = [-7 + 2] / [ -7 + 1 + 2 ]
-7 / [ -6] + 1/12 = [-5] / [-4] ???
14/12 + 1/12 = 5/4
15/12 = 5/4 and that checks
Check 3
3 / [ 3 + 1 ] + 1/12 = [3 + 2] / [ 3 + 1 + 2 ] =
3 / 4 + 1/12 = 5 / 6
9/12 + 1/12 = 5/6
10/12 = 5/6 yep....that works, too
So ..we get two answers......the fractions are 7/6 and 3/4
