Question

the numerator of a rational number is 5 less than the denominator. if the denominator is increased by 7and numerator 2, we gain get the same rational number. find the number​

Answer 1

Let the denominator be X so that numerator is x-7

Old rational number=x-7/x

and new rational number will be x-7+2/x+9=x-5/x+9

According to the condition of the problem,

x-7/x=x-5/x+9

(x-7)(x+9)=(x-5)(x)

x²-7x+9x-63=x²-5x

2x+5x=63

7x=63

x=9

Therefeore Rational number x-7/x=9-7/9=2/9

and new rational number=9-5/9+9=4/18=2/9

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