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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?

Verified Answer :

scme1702

(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

carlosego

For this case we have the following equation:
 \(\frac{3}{x} + \frac{1}{3} = \frac{5}{6}\)
 We multiply both sides of the equation by 3x:
 \(9 + x = \frac{5}{2}x\)
 We multiply both sides of the equation by 2:
 \(18+2x=5x\)
 From here, we clear the value of x:
 \(5x-2x=18 3x=18\)
 \(x = \frac{18}{3}\)
 \(x=6\)
 Answer:
 You can not divide by zero, but you can rewrite the expression to clear x.
 The value of x is given by:
 \(x=6\)

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