# How do you factor #2/3 = 2 - (5x-3)/(x-1)#?

Initially, we must simplify this as it is not in a form that can be recognized for factoring.

Take the denominators out:

This does not factorize and reduces to a straightforward linear equation.

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To factor the equation 2/3 = 2 - (5x-3)/(x-1), we can start by multiplying both sides of the equation by 3 to eliminate the fraction. This gives us 2 = 6 - (5x-3)/(x-1).

Next, we can multiply both sides of the equation by (x-1) to eliminate the fraction in the denominator. This gives us 2(x-1) = 6(x-1) - (5x-3).

Expanding the equation, we have 2x - 2 = 6x - 6 - 5x + 3.

Combining like terms, we get 2x - 2 = x - 3.

Moving all the terms to one side of the equation, we have 2x - x = -3 + 2.

Simplifying further, we get x = -1.

Therefore, the solution to the equation is x = -1.

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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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