Question

the numerator of a rational numer is 5 less than the denominator. if the denominator increase by 7 and numerator by 2. we again get the same rational number. find the number

Answer 1

let denominator be x
and numerator be x -5
A/Q
X+2/X-5+7=x/x-5
X+2/X+2=x/x-5
(x+2)(x-5)=x(x+2)
x^2-3x-10=x^2+2x
-3x-10=2X
-10=2x+3x
-10=5x
-10/5=x
-2=×

numerator =-7
denominator=-2

Answer 2

$(x - 5) \div x = (x - 5 + 2) \div (x + 7) \\ {x}^{2} - 3x = {x}^{2} + 2x - 35 \\ - 5x = - 35 \\ x = 7 \\ rational \: no . = 2 \div 7$
rational number 2/7