The denominator is 5 less than numerator.if 3 is added to numerator it

1.	The denominator is 5 less than numerator.if 3 is added to numerator it will be 11/6
Answer» Answer: $\huge\purple {\mathfrak{Bonjour Mate!}}$ Let the DENOMINATOR of FRACTION be x & numerator be x - 3 Fraction = numerator / denominator Fraction = (x - 3) / x……….(1) ATQ x - 3 / x+1 = (x -3 / x ) - 1/15 x - 3 / x+1 = [15 ( x- 3 ) - 1 × x] / 15x (x - 3 / x +1) =[ 15x - 45 - x] /15x 15x (x-3/x+1) = [ 14x - 45 ] 15x² - 45X = (14x - 45) (x +1) 15x² - 45x = x(14x - 45) + 1 (14x - 45) 15x² - 45x = 14x² - 45x + 14x - 45 15x² - 14x² - 45x + 45x - 14x + 45 x² - 14 x + 45 = 0 x² - 9x - 5x + 45 = 0 [By Middle term splitting] x(x- 9) - 5(x - 9) = 0 (x - 9) or (x-5)= 0 x= 9 or x = 5 If x = 9 Fraction = (x - 3) / x = (9-3)/9 = 6/9 If x= 5, then Fraction = (x - 3) / x = (5-3)/5 = ⅖ Hence, the fraction is 6/9 or ⅖.

The denominator is 5 less than numerator.if 3 is added to numerator it will be 11/6

Answer»

Answer:

$\huge\purple {\mathfrak{Bonjour Mate!}}$

& numerator be x - 3

Fraction = numerator / denominator

Fraction = (x - 3) / x……….(1)

ATQ

x - 3 / x+1 = (x -3 / x ) - 1/15

x - 3 / x+1 = [15 ( x- 3 ) - 1 × x] / 15x

(x - 3 / x +1) =[ 15x - 45 - x] /15x

15x (x-3/x+1) = [ 14x - 45 ]

15x² - 45X = (14x - 45) (x +1)

15x² - 45x = x(14x - 45) + 1 (14x - 45)

15x² - 45x = 14x² - 45x + 14x - 45

15x² - 14x² - 45x + 45x - 14x + 45

x² - 14 x + 45 = 0

x² - 9x - 5x + 45 = 0

[By Middle term splitting]

x(x- 9) - 5(x - 9) = 0

(x - 9) or (x-5)= 0

x= 9 or x = 5

If x = 9

Fraction = (x - 3) / x = (9-3)/9 = 6/9

If x= 5, then

Fraction = (x - 3) / x = (5-3)/5 = ⅖

Hence, the fraction is 6/9 or ⅖.