Question

The denominator of a fraction is greater than the numerator by 8 if the numerator is increased by 17 and denominator is decreased by 1 the number obtained is 3 by 2 find the fraction​

Answer 1

Let, the numerator of the fraction be, 'x'

The denominator is greater than the numerator by 8

So, the  is  denominator is = (x+8)

When the numerator gets increased by 17 then, the numerator becomes

= (x+17)

When the denominator gets decreased by 1 then the denominator becomes

= (x+8)-1

=(x+8-1)

= (x+7)

So, the new fraction obtained is = (x+17)/(x+7)

According to the problem,

(x+17)/(x+7) = 2/3

⇒ 3 × (x+17) = 2×(x+7)

[∵ When change the sides of the integers then the respective sign of the integers too gets changed such as, (+) to (-), (×) to (÷) and vice versa.]

⇒ 3x +51 = 2x +14

⇒ 3x-2x = 14-51

⇒ x = -47

So, the numerator is -47

∴ The denominator is = (-47+8)

                                   = -39

So, the fraction is = -47/-39

                            = 47/39

                           = 1 +(8/39)

Or, 1 whole of 8/39

[∵ (+)× (+) = (+)

(-)×(-) = (+)

(+)×(-) =(-)

(-)×(+) = (-)]

Answer 2

Answer:

The answer is 13/21

Step-by-step explanation:

according to the equation:

x+17/x+7=3/2

upon cross multiplication:

2(x+17)=3(x+7)

=> 3x - 2x = 43-21

=> x= 13

∴ x/x+8

=> 13/13+8 = 13/21