Question

The denominator of a fraction is 1 less than 3 times its numerator adding 3 to the numerator and denominator gives 1/2 . Find the fraction​

Answer 1

$\huge{\mathfrak{\underline{\red{Answer!}}}}$

Let numerator be x

denominator be y

y=3x-1 - - - - - - - - - - - - - equation 1

x/y + 1 =1/3 - - - - - - - - - - - equation 2

Substitute y in equation 2

x/3x-1 +1 =1/3

x+3x-1 =3x-1/3

3x+9x-3 =3x-1

12x-3x=3-1

9x =2

x=2/9

y=3*2/9 - 1

y=-1/3

the fraction =x/y

=2/9*-3/1

=-2/3

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Answer 2

Step-by-step explanation:

AnswEr :

Let us consider that Numerator be 'x'.

And, Denominator be '3x - 1'. [Denominator is 1 less than 3 times its denominator.]

$:\implies\tt Fraction = \dfrac{Numerator}{Denominator} = \dfrac{x}{3x - 1}$

☯ $\underline{\boldsymbol{According\: to \:the\: Question :}}$⠀

$:\implies\dfrac{x + 3}{3x - 1 + 3} = \dfrac{1}{2}\\\\\\:\implies\tt \dfrac{x + 3}{3x + 2}= \dfrac{1}{2} \\\\\\:\implies\tt 2\Big(x + 3 \Big) = 1 \Big( 3x + 2 \Big) \\\\\\:\implies\tt 2x + 6 = 3x + 2 \\\\\\:\implies\tt 2x + 6 - 3x -2 = 0 \\\\\\:\implies\tt x - 4 = 0 \\\\\\:\implies\tt x = 4\\\\\\:\implies\tt Now, \: fraction = \dfrac{x}{3x -1} = \dfrac{4}{3(4) - 1} \dfrac{4}{12 - 1} \\\\\\:\implies\tt \dfrac{4}{11}$

$\therefore\:\underline{\textsf{Required \: fraction \: is \: \textbf{ {} {\text4}\!/{}_{\text{11}} }}}.$