# How do you simplify #2/(x-2) div (x-1)/(4x - 8)#?

Begin by factorising 4x - 8 = 4(x - 2)

fraction now becomes

division of algebraic fractions is exactly the same as for numeric fractions.

and cancelling (x-2) gives

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To simplify the expression 2/(x-2) divided by (x-1)/(4x - 8), we can multiply the first fraction by the reciprocal of the second fraction.

Reciprocal of (x-1)/(4x - 8) is (4x - 8)/(x-1).

So, the expression simplifies to: 2/(x-2) * (4x - 8)/(x-1).

Next, we can simplify further by canceling out common factors between the numerators and denominators.

The numerator of the first fraction, 2, can be factored as 2 * 1.

The denominator of the first fraction, (x-2), and the numerator of the second fraction, (4x - 8), both have a common factor of 4.

The denominator of the second fraction, (x-1), and the numerator of the first fraction, 2, both have a common factor of 2.

After canceling out these common factors, the expression simplifies to:

(2 * 1 * (4x - 8))/(1 * 2 * (x-1)).

Simplifying further, we get:

(4x - 8)/(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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