# How do you multiply #(2x+2y)/(x+y) *( x^2-y^2)/(2x-2y)#?

Factoring:

Cancelling:

Further factoring:

Cancelling again:

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To multiply the given expression, you can follow these steps:

- Simplify both fractions individually, if possible.
- Multiply the numerators together and the denominators together.
- Simplify the resulting expression, if possible.

Let's apply these steps to the given expression:

- Simplify the fractions:
- The first fraction, (2x+2y)/(x+y), cannot be simplified further.
- The second fraction, (x^2-y^2)/(2x-2y), can be factored as (x+y)(x-y)/(2(x-y)).

- Multiply the numerators and denominators:
- Numerator: (2x+2y) * (x+y)(x-y)
- Denominator: (x+y) * 2(x-y)

- Simplify the resulting expression:
- The (x+y) terms in the numerator and denominator cancel out.
- The (x-y) terms in the numerator and denominator cancel out.
- The 2 in the denominator cancels out with one of the 2's in the numerator.

Note: It is important to mention that (x-y) cannot be equal to zero, as it would result in division by zero, which is undefined.

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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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