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How do you simplify #x / 3 - 2 / 3 = 1 / x#?

Answer 1

Nathan Axel

#color(green)(x = 3, -1#

#x/3 - 2/3 = 1/x#

#(x-2) / 3 = 1/x " taking 3 as L C M for L H S"#

#(x - 2) * x = 3 * 1, " cross multiplying"#

#x^2 - 2x = 3, " removing bracket"#

#x^2 - 2x - 3 = 0#

#x^2 + x - 3x - 3 = 0#

#x (x + 1) - 3 (x + 1) = 0#

# (x-3) * (x + 1) = 0#

#color(green)(x = 3, -1#

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Answer 2

Ethan Adkins

To simplify the equation x / 3 - 2 / 3 = 1 / x, we can start by getting rid of the fractions. Multiply both sides of the equation by the common denominator, which is 3x. This gives us x(x) - 2(x) = 3. Simplifying further, we have x^2 - 2x = 3. Rearranging the equation, we get x^2 - 2x - 3 = 0. This is a quadratic equation, which can be factored as (x - 3)(x + 1) = 0. Therefore, the solutions are x = 3 and x = -1.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.