Let's try to solve the equation:
1/x + 1/(x)² = 2
Kelly says that it is not possible because there are the variable x and x² in the denominators. Kelly is correct in that there is a value of x that makes the denominator zero. In this case, x = 0 makes the denominator of 1/x zero and also makes the denominator of 1/x² = 0.
But, we want to look for values of x that will make the whole equation true, not the values of x that make the denominators zero. 1/x + 1/(x)² = 2
(x +1)/(x)² = 2
Multiply through by x² with the proviso that x is not 0.
Then,
(x + 1) = 2x²
At this point, we are looking for solutions to (x + 1) = 2x² which is related to but not identical to the original equation. So, we will have to check any answers we get to
(x + 1) = 2x² against the original problem: 1/x + 1/(x)² = 2
