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

Suppose we want to solve the equation:
1/x + 1/(x)² = 2

Kelly says that it is impossible because there are the variable x and x² in the denominators. K 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 are looking for values of x that make the entire equation true, not values of x that make the denominators zero.

Answer 2

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

Answer 3

At this point, we are finding 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

Answer 4

Do you understand so far?

Answer 5

yeah i do

Answer 6

x = 1, x = -1/2