## The number of a factor is 3 less than its denominator.If 1 is added to the denominater the fraction is decreased by 1

Question

The number
of a factor is 3 less than its denominator.If 1 is
added to the denominater the fraction is
decreased
by 1 find the
the fraction​

in progress 0
2 weeks 2021-11-22T01:39:30+00:00 1 Answer 0 views 0

SOLUTION :

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.

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