Question

the denominator of a rational number is 2 less than twice the numerator. if the numerator and denominator are increased by 1 each, the rational number become 4 fraction 5 . find the number​

Answer 1

Step-by-step explanation:

By using the formula

Fraction = numerator/denominator

= (x – 3)/x

So, when numerator is increased by 2 and Denominator is increased by 5, then fraction is 1/2

(x – 3 + 2)/(x + 5) = 1/2

(x – 1)/(x + 5) = 1/2

By using cross-multiplication, we get

2(x – 1) = x + 5

2x – 2 = x + 5

2x – x = 2 + 5

x = 7

∴ Denominator is x = 7, numerator is (x – 3) = 7 – 3 = 4

And the fraction = numerator/denominator = 4/7

Answer 2

$\large\bf\underline\red{Answer \: :-}$

According to the question,

the denominator of a rational number is 2 less than twice the numerator.

$\sf{Denominator = 2x -2}$

$\sf{Numerator = x}$

if the numerator and denominator are increased by 1 each.

$\sf{Denominator = 2x-2+1 = 2x -1}$

$\sf{Numerator = x+1}$

the rational number become 4 fraction 5.

$\sf \bigstar{ \: \frac{x + 1}{2x - 1} = \frac{4}{5} }$

The number be x

Finding x

$\longmapsto\sf{5(x + 1) = 4(2x - 1)} \\ \longmapsto\sf{5 x + 5 = 8x - 4 } \: \: \: \: \: \: \: \: \: \\\longmapsto\sf{8x - 5x = 5 - 4} \: \: \: \: \: \: \: \: \\ \longmapsto\sf{3x = 1} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \longmapsto\sf{x = \boxed{ \frac{1}{3} }} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

_______________________________