# How do you solve #x/(2x-6)=2/(x-4)#?

Restrict the domain so that the solutions do not cause division by zero in the original equation.

Multiply both sides by both denominators.

Solve the resulting quadratic.

Check.

Limit the values of x such that no solutions are found that would result in division by zero:

Please note how the variables cancel out:

The equation with the cancelled factor subtracted is as follows:

On both sides, apply the distributive property:

These elements and the limitations are reversible:

Check:

This verifies.

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To solve the equation x/(2x-6) = 2/(x-4), we can start by cross-multiplying. This means multiplying the numerator of the first fraction by the denominator of the second fraction, and vice versa.

After cross-multiplying, we get x(x-4) = 2(2x-6).

Expanding both sides of the equation, we have x^2 - 4x = 4x - 12.

Combining like terms, we get x^2 - 8x + 12 = 0.

This quadratic equation can be factored as (x-6)(x-2) = 0.

Setting each factor equal to zero, we have x-6 = 0 or x-2 = 0.

Solving for x, we find x = 6 or x = 2.

Therefore, the solutions to the equation x/(2x-6) = 2/(x-4) are x = 6 and x = 2.

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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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