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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?

User Sheril
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2 Answers

5 votes
(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
User Lukaszrys
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7.9k points
4 votes
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
User CalgaryFlames
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