Question

the numerator of a fraction is 1 less than its denominator ,of the numerator is increased by 4 and the denominator is increased by 5 the new fraction becomes equivalent to four-fifth what is the original fraction. frame equation

Answer 1

let denominator = x
numerator = x-1
fraction= x-1/x
the numerator increased by 4= x-1+4
= x+3
denominator = x+5
fraction= x+3/x+5
x+3/x+5 = 4/5 (x-1/x)
5(x+3/x+5) = 4(x-1/x)
5x+15/x+5 = 4x-4/x
5x^2 + 15x = (x+5)(4x-4)
5x^2+15x = 4x^2 -4x+20x-20
x^2+15x-16x-20
x^2-x-20
x^2-5x+4x-20=0
x(x-5) +4(x-5)=
(x-5)(x+4)=0
x-5=0, x+4=0
x=5,-4
x=5 is taken
orginal fraction = x-1/x
substitute x=5 in above
5-1/5
4/5 is answer