Question

A fraction is such that the numerator is 2 less than the denominator. If you add 3 to the numerator and 5 to the denominator, the resulting fraction is equivalent to the fraction. Find the original fraction.

Answer 1

Answer:

x-2/x

After adding 3 to numerator and 5 to the denominator resulting fraction is equals to the original fraction -

therefore -

x-2+3/x+5 = x-2/x

x+1/x+5 = x-2/x

Now by cross multiplication

(x+1)(x) = (x-2)(x+5)

x^2 + x = x^2 + 5x - 2x - 10

x = 5x - 2x - 10

x = 3x - 10

x - 3x = -10

-2x = -10

x = -10/-2

x = 5

Verification -

By putting the value of x we get -

5-2+3/5+5 = 5-2/5

3+3/10 = 3/5

6/10 = 3/5

3/5 = 3/5

Therefore the fraction is 3/5

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Step-by-step explanation: