Question

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

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Step-by-step explanation:Let the numerator be x

The denominator is x + 7

Define the fraction:

The fraction is x/(x + 7)

Solve x:

The denominator increased by 9 and numerator decreased by 2, we can the same number

(x + 2) / ( x+ 7 + 9) = x / (x + 7)

(x + 2) / ( x+ 16) = x / (x + 7)

(x + 2) ( x + 7) = x (x + 16)

x² + 9x + 14 = x² + 16x

16x - 9x = 14

7x = 14

x = 2

Find the fraction:

Numerator = x = 2

denominator = x + 7 = 2 + 7 = 9

Find the fraction:

Fraction = 2/9

Answer: The fraction is 2/9