Question

the numerator of a fraction is 7 less than the denominator. if the denominator is increased by 2 and the denominator by 9 we again get the same fraction . find the fraction​

Answer 1

I think there is a mistake in the question.

Answer:The fraction is 2/9 .

Step by step explanation:

let, the denominator of the fraction be x.

So, numerator = x - 7

Fraction = x - 7/x

Again,

Denominator = x + 9

Numerator = ( x - 7 ) + 2 = x -5

According to question,

$\frac{x - 7}{x} = \frac{x - 5}{x + 9} \\ \\ (x - 7)(x + 9) = x(x - 5) \\ \\ {x}^{2} + 9x - 7x - 63 = {x}^{2} - 5x \\ \\ 2x + 5x = 63 \\ \\ 7x = 63 \\ \\ x = 9$

So, Fraction = x-7/x = 9-7/9= 2/9 .