# How do you solve # 1/(4 -x) = x/8#?

Below

Using the quadratic formula:

If you haven't learnt complex numbers yet, then you can ignore the following lines and just state that since the discriminant is less than 0, then there is no solution to the equation.

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To solve the equation 1/(4 - x) = x/8, you can start by cross-multiplying to eliminate the fractions. Multiply both sides of the equation by (4 - x) and 8 to get rid of the denominators. This will give you 8 = x(4 - x). Simplify the equation by distributing x, which results in 8 = 4x - x^2. Rearrange the equation to form a quadratic equation: x^2 - 4x + 8 = 0. To solve this quadratic equation, you can use factoring, completing the square, or the quadratic formula. In this case, the quadratic equation does not factor easily, so you can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a). Plugging in the values from the quadratic equation, you will get x = (4 ± √(-16)) / 2. Since the discriminant (b^2 - 4ac) is negative, the equation has no real solutions. Therefore, there are no real values of x that satisfy the original equation 1/(4 - x) = x/8.

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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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