How do you solve #6/(x^2-8x) = 1/x + 3/(x^2-8x)# and find any extraneous solutions?

Answer 1

Solution: #x=11#

# 6/(x^2-8x) = 1/x + 3/(x^2-8x) or #
# 6/(x^2-8x) - 3/(x^2-8x) = 1/x or#
# (6-3)/(x^2-8x) = 1/x or 3/(x^2-8x) = 1/x# or
#x^2-8x=3x or x^2-11x =0# or
#x(x-11)=0 #. Eeither #x=0 or x-11= 0 :. x=11#
#1/x or 3/(x^2-8x) # is undefined for #x=0 :. x != 0#
Solution: #x=11# [Ans]
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Answer 2

To solve the equation 6/(x^2-8x) = 1/x + 3/(x^2-8x) and find any extraneous solutions, we can follow these steps:

  1. Start by finding a common denominator for the fractions on the right side of the equation, which is x(x^2-8x). Rewrite the equation as follows: 6/(x^2-8x) = (x(x^2-8x) + 3)/(x(x^2-8x))

  2. Multiply both sides of the equation by the common denominator (x^2-8x) to eliminate the denominators: 6 = x(x^2-8x) + 3

  3. Expand and simplify the equation: 6 = x^3 - 8x^2 + 3x + 3

  4. Rearrange the equation to have all terms on one side: x^3 - 8x^2 + 3x + 3 - 6 = 0 x^3 - 8x^2 + 3x - 3 = 0

  5. Now, we need to solve this cubic equation. Unfortunately, there is no general formula to solve cubic equations, so we'll need to use numerical methods or factorization techniques to find the solutions.

  6. After solving the equation, we obtain the values of x. However, we need to check if any of these solutions are extraneous, meaning they make the original equation undefined.

  7. To check for extraneous solutions, substitute each solution back into the original equation and see if any denominator becomes zero. If a denominator becomes zero, that solution is extraneous and should be discarded.

This is the process to solve the equation and find any extraneous solutions.

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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.

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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