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." How will you show Amanda that the equation is still solvable and explain your reasoning?

Answer 1

(3 / x) + (1/3) = (5 / 6)
Taking the LCM on the left side
(9 + x)/(3x) = (5/6)
54 + 6x = 15x
From this step, it is visible that x is no longer in th denominator and even if it is 0, the equation is solvable.
9x = 54
x = 6

Answer 2

For this case we have the following equation:

`(3)/(x) + (1)/(3) = (5)/(6)`
We multiply both sides of the equation by 3x:

`9 + x = (5)/(2)x`
We multiply both sides of the equation by 2:

`18+2x=5x`
From here, we clear the value of x:

`5x-2x=18 3x=18`

`x = (18)/(3)`

`x=6`
Answer:
You can not divide by zero, but you can rewrite the expression to clear x.
The value of x is given by:

`x=6`