# How do you simplify #((x)/(x+1))/(x+x/3)#?

First, add the terms in the denominator.

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To simplify ((x)/(x+1))/(x+x/3), we can follow these steps:

- Simplify the expression within the parentheses: (x)/(x+1) becomes x/(x+1).
- Simplify the expression x+x/3: To add x and x/3, we need a common denominator, which is 3. So, x+x/3 becomes (3x+x)/3, which simplifies to (4x)/3.

Now, we can rewrite the expression as x/(x+1) divided by (4x)/3.

To divide by a fraction, we multiply by its reciprocal. Therefore, we can rewrite the expression as x/(x+1) multiplied by 3/(4x).

Now, we can simplify further by canceling out common factors. The x in the numerator and denominator cancels out, leaving us with 1/(x+1) multiplied by 3/4.

So, the simplified expression is (3/4)/(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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