Question

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The numerator of a rational number is 7 less than the denominator. If the denominator is increased by 9 and the
numerator by 2, we get the same rational number. Find the number.​

Answer 1

Hey dude here is your Answer------------------------ ✔️❣️✔️ ❣️✔️ ❣️✔️ ❣️

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

✔️✔️Hope it helps you ✔️✔️

Answer 2

Answer:

2/9.

Step-by-step explanation:

Let the rational number be =n/p

Again, p-7=n

or, p=n+7

So rational number=n/(n+7)

Now, new rational number =(n+2)/(n+16)

Again, n/n+7=n+2/n+16

n²+16n=n²+9n+14

or, 16n=9n+14

or, 7n=14

or, n=2

So, the number =2/9.