Question

The denominator of a rational number is greater than its numerator by 3. If 3 is subtracted from the numerator and 2 is added to its denominator, the new number becomes original rational number.

Answer 1

Answer:

Numerator = -9/5

Denominator = 6/5

Step-by-step explanation:

Let the numerator be x.

Then,denominator is greater than numerator by 3

i.e., denominator = x + 3

The rational number will be   $\frac{x}{x+3}$

Now,3 is subtracted from numerator then numerator becomes = x - 3

2 is added to denominator,then denominator becomes = x + 3 + 2 = x + 5

The rational number = $\frac{x-3}{x+5}$ which is equal to original rational number (given)

$\frac{x}{x+3} =\frac{x-3}{x+5} \\ \\ x(x+5) = (x-3)(x+3) \\\\ x^{2} + 5x = x^{2} - 3^{2} \\\\5x=-9\\\\x = \frac{-9}{5} \\\\ The \ numerator= \frac{-9}{5} \\ The \ denominator=x+3 = \frac{-9}{5} + 3 = \frac{6}{5} \\\\ The \ rational \ number = \frac{\frac{-9}{5} }{\frac{6}{5} } = \frac{-9}{6}$