How do you solve #3/(2x-1) - 4/(3x-1) = 1#?

Answer 1

#3(3x-1)-4(2x-1)=1(2x-1)(3x-1) ->9x-3-8x+4=6x^2-5x+1#
#0=6x^2-6x ->6x(x-1)=0,6x=0 or x-1 = 0, x=0 or x=1#

Multiply everything on both sides by the common denominator then put everything on one side and solve for x

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Answer 2

To solve the equation 3/(2x-1) - 4/(3x-1) = 1, you 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 (2x-1)(3x-1).

  2. Multiply each term by the common denominator to eliminate the fractions. This gives you: 3(3x-1) - 4(2x-1) = (2x-1)(3x-1).

  3. Simplify both sides of the equation by distributing and combining like terms. This results in: 9x - 3 - 8x + 4 = 6x^2 - 5x + 1.

  4. Combine like terms on both sides of the equation. This gives you: x + 1 = 6x^2 - 5x + 1.

  5. Rearrange the equation to bring all terms to one side and set it equal to zero. This gives you: 6x^2 - 6x = 0.

  6. Factor out the greatest common factor, which is 6x. This results in: 6x(x - 1) = 0.

  7. Apply the zero product property, which states that if a product of factors is equal to zero, then at least one of the factors must be zero. Set each factor equal to zero and solve for x.

    • 6x = 0 --> x = 0
    • x - 1 = 0 --> x = 1

Therefore, the solutions to the equation 3/(2x-1) - 4/(3x-1) = 1 are x = 0 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.

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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