Self Maths Puzzle Numerical Ability

Given that x+y+xy=1, where x and y are nonzero real numbers,find the value of xy+1/xy−y/x−x/y.

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Self Other Question

a binary communication channel carries data as one of the two types of signals denoted by 'a' and 'b'. owing to noise a transmitted 'a' is sometimes received as 'b' and a transmitted 'b' is sometimes received as 'a'. for a given channel assume a probability of 0.94 that a transmitted 'a' is correctly received as 'a' and the probability of 0.91 that a transmitted 'b' is received as 'b' further assume a probability of 0.45 of transmitting a 'a'. If a signal is sent,determine probability that 'b' is received. probability that 'b' was transmitted given that 'a' was received Given that
a+b+c=1
a^2+b^2+c^2=2
a^3+b^3+c^3=3
If a^4+b^4+c^4= x/y where x & y are positive coprime integers, then find x+y