Question

The numerator of a fraction is 6 less than the denominator. If 3 is added to the numerator, the fraction becomes equal to 2/3 . Find the original fraction.

Answer 1

Hey MATE!

Let the denominator of the fraction be x, therefore the numerator of the fraction is
(x - 6).

Now 3 is added to both of them:

$\frac{(x - 6) + 3}{x + 3} = \frac{2}{3} \\ \frac{x - 3}{x + 3} = \frac{2}{3} \\ \\ 3(x - 3) = 2(x + 3) \\ \\ 3x - 9 = 2x + 6 \\ \\ 3x - 2x = 9 + 6 \\ x = 15 \\ \\ therefore \: fraction \: is \\ = > \frac{15 - 6}{15} \\ = > \frac{9}{15} \: answer$
Hope it helps

Hakuna Matata :))

Answer 2

$\circ\circ\circ\circ\underline{\fbox{\fbox{\fbox{\fbox{\fbox{\Large{\underline{\textbf{SOLUTION}}}}}}}}}\circ\circ\circ\circ$

$Let\:the\:denominator\:be\:x\\\\then\:numerator=x-6\\\\\\According\:to\:question,\\\\\\\implies(x-6)+\frac{3}{x}=\frac{2}{3}\\\\\implies\frac{(x-6+3)}{x}=\frac{2}{3}\\\\\implies\frac{(x-3)}{x}=\frac{2}{3}\\\\\\\implies3(x-3)=2x\:[by\:cross\:multiplication]\\\\\implies3x-9=2x\\\\\implies3x-2x=9\\\\\implies \boxed{x=9\:(denominator)}\\\\\\Numerator\\\\\implies x-6\\\\\boxed{=9-6=3\:(Numerator)}\\\\the\:fraction=\frac{3}{9}$