Question

the numerator of a factor is 3 less than its denominator . if 1 is added to the denominator , the fraction is decreased by 1/15. Find the fraction ​

Answer 1

Step-by-step explanation:

ANSWER

Let the denominator be x then numerator be (x-3)

fraction =

x

x−3

It is added ⇒

x+1

x−3

=

x

x−3

−

15

1

(by the condition)

⇒

x+1

x−3

=

15x

15x−45−x

.

⇒

x+1

x−3

=

15x

14x−45

⇒15x

2

−45x=14x

2

−45x+14x−45

⇒x

2

−14x+45=0

⇒x

2

−9x−5x+45=0

⇒x(x−9)−5(x−9)=0

⇒x−5=0,x−9=0

∴x=5,9.

If x = 9 ⇒ fraction =

9

9−3

=

9

6

=

3

2

If x = 5 ⇒ fraction =

5

5−3

=

5

2

Hence . the fraction is

5

2

or

3

2

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