Question

(((pq)/(p²-q²)+(q)/(q-p)))/((p-q+((4q²-p²))/(p+q)))

a. find the if statement, like p cannot be q or something like that

Answer 1

The expression is undefined when p equals q or when p+q=0.

The given expression contains fractions and involves operations that result in a denominator with terms that could potentially lead to division by zero. To identify the conditions under which the expression is undefined, we set the denominators of the fractions in the expression equal to zero.

The first denominator is (p^2 −q^2), and the second denominator is (p−q+ 4q^2−p^2/p+q ​). The expression is undefined when either of these denominators equals zero.

For the first denominator, p^2 −q^2, the expression is undefined when p equals q since it results in a zero denominator.

For the second denominator, 4q^2 −p^2/p+q, the expression is undefined when p+q=0, as this would also result in a zero denominator.

Therefore, the conditions for the expression to be undefined are when p equals q or when p+q=0. It's crucial to avoid these values to ensure the expression remains well-defined and doesn't result in division by zero.