Question

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

Answer 1

Step-by-step explanation:

1. Let the numerator of the rational number be x.

So as per the given condition, the denominator will be x + 8.

The rational number will be \(\frac{x}{x+8}\)

According to the given condition,

\(\frac{x+17}{x+8-1} = \frac{3}{2}\)

 

\(\frac{x+17}{x+7} = \frac{3}{2}\)

 

3(x + 7) = 2(x + 17)

3x + 21 = 2x + 34

3x – 2x + 21 – 34 = 0

x – 13 = 0

x = 13

The rational number will be

= \(\frac{x}{x+8}\)

= \(\frac{13}{13+8}\)

Rational number = 13/21

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Answer 2

Answer:

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 decreased 9 and numerator 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);

x ^ 2 + 9x + 14 = x ^ 2 + 16x;

16x - 9x = 14;

7x = 14; x = 2

Find the fraction:

Numerator Or = x = 2

denominator =x+7=2+7=9

Find the fraction: Fraction = 2/9

Answer: The fraction is 2/9