y/(1/xy+1)

Question

its algebra 2

Answer 1

It's not clear whether the denominator is   1/(xy) + 1   or   1/(xy + 1).

In the case of the former, since we are essentially adding fractions we need to find a common denominator among them. Here, the common denominator is 'xy' so we need to multiply 1 by xy/xy then add the fractions in the denominator:

     y/(1/(xy) + 1) = y/(1/(xy) + 1(xy/xy))

                         = y/(1/(xy) + (xy)/(xy))

                         = y/((1 + xy)/(xy))

When dividing by a fraction, multiply the numerator by the reciprocal of the denominator:

          y/((1 + xy)/(xy)) = y((xy)/(1 + xy)

                                   = (y·xy)/(1 + xy)

                                   = xy²/(1 + xy)

In the second case, since we don't need to add any fractions we simply multiply the numerator by the reciprocal of the denominator:

          y/(1/(xy + 1)) = y((xy + 1)/1)

                              = y(xy + 1)

                              = y·xy + y·1

                              = xy² + y   

    

Answer 2

y/(1/(xy) +1)   Get same denominator on the bottom

y/ ((1+xy)/xy)  Turn the division sign into multiplication and flip the bottom

y* (xy)/ (1+xy)  Simplify

= xy^2/(1+xy)