Question

The numerator of a fraction is 2 less than its denominator if 1 is added to the both numerator and denominator the sum of the new and original fraction as 19 by 15 find the original fraction

Answer 1

let the numerator be x

then the denominator=x+2

it is given that x/x+2+x+1/x+3=19/15

                        x(x+3)+(x+1)(x+2)/(x+2)(x+3)=19/15

                        x^2+3x+x^2+3x+2/x^2+5x+6=19/15

                        2x^2+6x+2/x^2+5x+6=19/15

                        30x^2+90x+30=19x^2+95x+114

                        11x^2-5x-84=0

                        11x^2-33x+28x-84=0

                        11x(x-3)+28(x-3)=0

                        (11x+28)(x-3)=0

                        x=-28/11 or x=3

                      original fraction=3/5