Help with fractions?

Question

Can anyone help me with this fraction word problem? Thanks.

the denominator of a fraction is an integer that is one greater than the numerator. a second fraction is the reciprocal of the integer that is one less than the numerator of the first fraction. if the product of the two fractions is 3/8 identify the first fraction.

Answer 1

Let the numarator of a fraction  = x

Denomnator is one greater than the numerator, so x+1 is denominator.

Where x is an integer.

So the first fraction is x/(x+1)

Also second fraction is 1/(x-1).

Product of two fractions is 3/8.

x/(x+1)*1/(x-1) = 3/8

x/(x^2-1) = 3/8

Cross multiplication.

8x = 3(x^2-1)

8x = 3x^2-3

3x^2-8x-3 = 0

3x^2-9x+x-3 = 0

3x(x-3)+1(x-3) = 0

(x-3)(3x+1) = 0

x = 3 and 3x = -1

But x is an integer.

So x = 3

the fractions are 3/4 and 1/2

First fraction is 3/4.