# How do you simplify #(ax - ay - 2by + 2bx)/(ax - 2bx + 2by + ay)#?

This cannot, in my opinion, be overly simplified:

I experimented by combining coefficients as follows:

I then noticed that the same coefficient was present in three of the four terms, so I divided by it:

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To simplify the expression (ax - ay - 2by + 2bx)/(ax - 2bx + 2by + ay), we can factor out common terms from both the numerator and the denominator.

First, let's factor out an 'a' from the numerator and the denominator: (ax - ay - 2by + 2bx)/(ax - 2bx + 2by + ay) = (a(x - y) - 2b(y - x))/(a(x - y) - 2b(x - y))

Next, we can simplify further by canceling out the common factor of (x - y) from both the numerator and the denominator: (a(x - y) - 2b(y - x))/(a(x - y) - 2b(x - y)) = (a - 2b)/(a - 2b)

Therefore, the simplified expression is (a - 2b)/(a - 2b).

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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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