Question

Amanda tells you that because a variable is in the denominator, the equation three over x plus one over three equals five over six becomes unsolvable. Amanda explains, "There is a value for x that makes the denominator zero, and you can't divide by zero." Demonstrate to Amanda how the equation is still solvable and explain your reasoning.

Answer 1

3/x + 1/3 = 5/6
3/x = 5/6 - 1/3
3/x = 5/6 - 2/6
3/x = 1/2....multiply both sides by x, eliminating the x on the left side
3 = 1/2x...now multiply both sides by 2, eliminating the 1/2 on the right side
3 * 2 = x
6 = x

check..
3/6 + 1/3 = 5/6
3/6 + 2/6 = 5/6
5/6 = 5/6 (correct)

so x = 6

Answer 2

x = 6 .................................................