Question

Kelly tells you that when variables are in the denominator, the equation becomes unsolvable. "There is a value for x that makes the denominator zero, and you can't divide by zero," Kelly explains. Using complete sentences, demonstrate to Kelly how the equation is still solvable.

Answer 1

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