Question

Cot c/2=____________​

Answer 1

$\large \dag$ Question :-

Numerator of a fraction is 2 less than the denominator If 1 is added to the numerator and 3 to the denominator then the fraction becomes 2/3. Find the original fraction.

$\large \dag$ Answer :-

$\red\dashrightarrow\underline{\underline{\sf  \green{The   \: Original \:  Fraction  \: is \:  \frac{7}{9} }} }$

$\large \dag$ Step by step Explanation :-

Let Numerator and Denominator of Original Fraction be :

Numerator = x

As Per the question numerator of the fraction is 2 less than the denominator so,

Denominator should be = x + 2

So ,

$\text{Original Fraction = } \frac{\text x}{\text x + 2}$

❒ When 1 is added to the numerator and 3 to the denominator :

$\rm \text{Fraction Becomes } :  \frac{x + 1}{x + 5}$

⏩ According To Question :

$\large \blue \bigstar  \:   \red{ \bf  \frac{x + 1}{x + 5} =  \frac{2}{3}  }$

$:\longmapsto \rm 3(x + 1) = 2( + 5)$

$:\longmapsto \rm 3x + 3 = 2x + 10$

$:\longmapsto \rm 3x - 2x = 10 - 3$

$\purple{ \large :\longmapsto  \underline {\boxed{{\bf x = 7} }}}$

$\blue\dashrightarrow\underline{\underline{\sf  \orange{Numerator  \: of \:  Original  \: Fraction = 7 }} }$

☆ As numerator of the fraction is 2 less than the denominator :

$\rm\therefore \:  Denominator  = 7   + 2$

$\blue\dashrightarrow\underline{\underline{\sf  \orange{Denominator  \: of \:  Original  \: Fraction = 9 }} }$

Therefore,

$\large\underline{\pink{\underline{\frak{\pmb{ Original  \: Fraction  =  \dfrac{7}{9} }}}}}$