Question

The denominator of a rational number is greater than its numerator by 4. if the number in increased by 15 and the denominator is decreased by 1 the number obtained 6/5. Find tge rational number

with steps​

Answer 1

${\tt{\underline{Given :-}}}$

The denominator of a rational number is greater than its numerator by 4. if the number is increased by 15 and the denominator is decreased by 1 the number is obtained 6/5.

${\tt{\underline{Need\;to\;find:-}}}$

The rational number

${\tt{\underline{Answer:-}}}$

Firstly, we have to assume the rational number's numerator as a variable that is x. The Denominator is 4 greater than its numerator. Denominator = (x + 4)

x + 15/(x + 4) - 1 = 6/5

x + 15/x + 3 = 6/5

5(x + 15) = 6(x + 3)

5x + 75 = 6x + 18

5x - 6x = 18 - 75

-x = -57

x = 57

Numerator =

x

57

Denomiantor =

x + 4

57 + 4

61

Fraction

57/61

Answer 2

Step-by-step explanation:

let the rational number = x/y

if denominator is 4 great than numerator

x + 4 = y

therefore

rational number = x/x+4

if numerator is increased by 15 and denominator is decreased by 1 = 6/5

therefore,

x+15/x+4-1 = 6/5

x + 15 = 6

x = 6 -15

x = -9

y = x +4

y = (-9) + 4

y = -5

rational number = x/y = -9/-5 = 9/5