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

Answer 1

#"x"=2#
#"x"=-12#

What is the least common denominator of 3, x and 6? 6x 1. Multiply everything by 6x to clear out the denominator. #6x(4/x-5/3=x/6)# #(24-10x=x^2)# 2. Looks like a quadratic, solve by factoring #x^2+10x-24=0# #(x-2)(x+12)=0# #"x"=2# #"x"=-12#
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Answer 2

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

  1. Find a common denominator for the fractions on the left side of the equation. In this case, the common denominator is 3x.
  2. Multiply each term by the common denominator to eliminate the fractions. This gives us: (4 * 3) - (5 * x) = (x * 3x) / 6.
  3. Simplify the equation: 12 - 5x = 3x^2 / 6.
  4. Simplify further: 12 - 5x = x^2 / 2.
  5. Multiply both sides of the equation by 2 to eliminate the fraction: 24 - 10x = x^2.
  6. Rearrange the equation to bring all terms to one side: x^2 + 10x - 24 = 0.
  7. Factorize the quadratic equation: (x + 12)(x - 2) = 0.
  8. Set each factor equal to zero and solve for x: x + 12 = 0 or x - 2 = 0.
  9. 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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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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