Question

The numerator of a rational number is five less than the denominator. If the denominator is increased by seven,The numerator by two, we again get the same rational number. Find the rational number

Answer 1

Answer:

Step-by-step explanation:

let the denominator be x

so the numerator will be x-5  

and the rational number become (x-5)/x

now according to the question the denominator becomes x+7

Answer 2

Answer:2/7

Step-by-step explanation:

Let the denominator be x.

According to the given condition,

x-5/x. .......(1)

(x-5)+2 / x+7

=x-3 / x+7 .....(2)

Combining (1) and (2),

x-5. / x = x-3 / x+7

(x -5) (x+7) = x(x-3)

x^2 + 7x -5x -35 = x^2 - 3x

x^2 + 2x - 35 = x^2 - 3x

x^2 - x^2 + 2x +3x = 35

5x=35

x=35/5

x=7

By substituting x=7 in (1).,we get

7-5 / 7 =2/7

Therefore the required rational no. = 2/7

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