Question

The denominator of a fraction is 2 more than the numerator. If 1 is added to each of the numerator and the denominator of the fraction, then the fraction becomes 3/4. Find the original fraction?​

Answer 1

Step-by-step explanation:

we will let it as x x+1/x+3=3/4

Answer 2

Answer :-

• Original fraction => 5/7

Given :-

• The denominator of a fraction is 2 more than the numerator. If 1 is added to each of the numerator and the denominator of the fraction, then the fraction becomes 3/4.

To Find :-

• The original fraction.

Step By Step Explanation :-

As given in the question the denominator of a fraction is 2 more than the numerator. If 1 is added to each of the numerator and the denominator of the fraction, then the fraction becomes 3/4.

Let us consider the numerator be x and the denominator be x + 2.

Now, Equation will be ⤵

${ \boxed{ \boxed {\purple { \bf{\cfrac{x + 1}{x + 2 + 1} = \cfrac{3}{4} }}}}}$

Now let's solve this equation !!

$\implies\sf \cfrac{x + 1}{x + 2 + 1} = \cfrac{3}{4} \\ \\ \implies\sf \cfrac{x + 1}{x + 3} = \cfrac{3}{4} \\ \\ \implies\sf4(x + 1) = 3(x + 3) \\ \\ \implies\sf4x + 4 = 3x + 9 \\ \\ \implies\sf4x - 3x = 9 - 4 \\ \\ \implies\bf {\green{ x = 5}}$

Now x = 5

By substituting the value of x ⤵

$\sf \cfrac{x}{x + 2} \implies \cfrac{5}{5 + 2} \implies \bf \cfrac{5}{7}$

Hence original fraction = 5/7

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