# How do you solve #4/x-5/3=x/6#?

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To solve the equation 4/x - 5/3 = x/6, we can follow these steps:

- Find a common denominator for the fractions on the left side of the equation. In this case, the common denominator is 3x.
- Multiply each term by the common denominator to eliminate the fractions. This gives us: (4 * 3) - (5 * x) = (x * 3x) / 6.
- Simplify the equation: 12 - 5x = 3x^2 / 6.
- Simplify further: 12 - 5x = x^2 / 2.
- Multiply both sides of the equation by 2 to eliminate the fraction: 24 - 10x = x^2.
- Rearrange the equation to bring all terms to one side: x^2 + 10x - 24 = 0.
- Factorize the quadratic equation: (x + 12)(x - 2) = 0.
- Set each factor equal to zero and solve for x: x + 12 = 0 or x - 2 = 0.
- Solve for x in each equation: x = -12 or x = 2.

Therefore, the solutions to the equation 4/x - 5/3 = x/6 are x = -12 and x = 2.

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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.

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.

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.

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