# How do you simplify the expression #(y-12/(y-4))/(y-18/(y-3))#?

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I chose to multiply by a form of 1 that eliminates the complex fractions but there may be a better way, because I, later, discover a common factor that becomes 1.

Multiply the two fractions:

Distribute y:

Distribute 12 and 18:

Combine like terms:

I asked WolframAlpha to factor the numerator and obtained the following answer:

Then I asked WolframAlpha to factor the denominator and obtained the following answer:

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# (y-12/(y-4))/(y-18/(y-3)) =((y+2)(y-3))/((y+3)(y-4)) #

We want to simplify:

Firstly consider the numerator, which we can simplify by putting over a common denominator, thus:

Secondly consider the denominator, which we can also simplify by putting over a common denominator, thus:

So now we can rewrite the expression as:

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To simplify the expression (y-12/(y-4))/(y-18/(y-3)), you can start by simplifying each fraction separately.

For the first fraction, y-12/(y-4), you can simplify it by factoring out a common factor of (y-4) from the numerator and denominator. This gives you (y-12)/(y-4) = (y-4-8)/(y-4) = (y-4)/(y-4) - 8/(y-4) = 1 - 8/(y-4).

For the second fraction, y-18/(y-3), you can simplify it in a similar way. Factor out a common factor of (y-3) from the numerator and denominator to get (y-18)/(y-3) = (y-3-15)/(y-3) = (y-3)/(y-3) - 15/(y-3) = 1 - 15/(y-3).

Now, you can substitute these simplified fractions back into the original expression: (1 - 8/(y-4))/(1 - 15/(y-3)).

To simplify further, you can find a common denominator for the two fractions, which is (y-4)(y-3). Multiply the numerator and denominator of the first fraction by (y-3) and the numerator and denominator of the second fraction by (y-4). This gives you ((y-3) - 8)/(y-4) and ((y-4) - 15)/(y-3).

Simplifying these fractions further, you get (y-3-8)/(y-4) = (y-11)/(y-4) and (y-4-15)/(y-3) = (y-19)/(y-3).

Finally, substitute these simplified fractions back into the expression: (y-11)/(y-4) / (y-19)/(y-3).

To divide fractions, you can multiply the first fraction by the reciprocal of the second fraction. This gives you (y-11)/(y-4) * (y-3)/(y-19).

Multiply the numerators together and the denominators together: (y-11)(y-3)/(y-4)(y-19).

This is the simplified expression: (y-11)(y-3)/(y-4)(y-19).

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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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