Question

The numerator of a fraction is 3 less than the denominator. If 7 is added to the numerator, the value of the fraction increases by 1. Find the fraction.

Answer 1

Answer is in attachment

pls follow and mark brainliest

Answer 2

Answer:

$\displaystyle{\boxed{\red{\sf\:The\:fraction\:=\:\dfrac{4}{7}}}}$

Step-by-step-explanation:

Let the numerator of the fraction be x.

And the denominator of the fraction be ( x + 3 ).

$\displaystyle{\sf\:\therefore\:The\:fraction\:=\:\dfrac{x}{(\:x\:+\:3\:)}}$

From the given condition,

$\displaystyle{\sf\:\dfrac{x\:+\:7}{x\:+\:3}\:=\:\dfrac{x}{(\:x\:+\:3\:)}\:+\:1}$

$\displaystyle{\implies\sf\:\dfrac{x\:+\:7}{x\:+\:3}\:=\:\dfrac{x\:+\:(\:x\:+\:3\:)}{x\:+\:3}}$

$\displaystyle{\implies\sf\:\dfrac{x\:+\:7}{x\:+\:3}\:=\:\dfrac{x\:+\:x\:+\:3}{x\:+\:3}}$.

$\displaystyle{\implies\sf\:\dfrac{x\:+\:7}{\cancel{(\:x\:+\:3\:)}}\:=\:\dfrac{2x\:+\:3}{\cancel{(\:x\:+\:3\:)}}}$

$\displaystyle{\implies\sf\:x\:+\:7\:=\:2x\:+\:3}$

$\displaystyle{\implies\sf\:7\:-\:3\:=\:2x\:-\:x}$

$\displaystyle{\implies\boxed{\red{\sf\:x\:=\:4}}}$

The numerator of the fraction ( x ) = 4

And the denominator of the fraction ( x + 3 ) = ( 4 + 3 ) = 7

$\displaystyle{\therefore\:\underline{\boxed{\red{\sf\:The\:fraction\:=\:\dfrac{4}{7}}}}}$