Question

the numerator of a rational number is 3 less than the denominator.if the denominator is increased by5 and the numerator by 2,we get the rational number1/2 find the rational number

Answer 1

Let the rational number be x/y.
x+3=y.Then,
x/y=x/x+3
If numerator increased by 2 and denominator by 5,then,
x+2/x+3+5
x+2/x+8=1/2
x+2=1/2×(x+8)
2(x+2)=x+8
2x+4=x+8
2x-x=8-4
x=4.Then,the rational number is,
x/x+3
4/7.
The rational number is 4/7.