# How do you simplify #(5x) /(x^2 - 9)*(6x + 18) / (15x^3)#?

the answer is

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To simplify the expression (5x) /(x^2 - 9)*(6x + 18) / (15x^3), we can cancel out common factors in the numerator and denominator.

First, let's factor the expressions: x^2 - 9 can be factored as (x + 3)(x - 3). 15x^3 can be factored as 3x^3 * 5.

Now, let's cancel out the common factors: In the numerator, we have 5x and 6x + 18. Both have a common factor of x, so we can cancel out the x.

In the denominator, we have (x + 3)(x - 3) and 3x^3 * 5. The (x + 3) term cancels out with one of the x terms in 3x^3, and the (x - 3) term cancels out with the remaining x term in 3x^3. Additionally, the 5 in the denominator cancels out with the 5 in the numerator.

After canceling out the common factors, we are left with: (5 * 1) / (1 * 3x^2) which simplifies to: 5 / 3x^2

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To simplify the expression (\frac{5x}{x^2 - 9} \times \frac{6x + 18}{15x^3}), we can follow these steps:

- Factor any expressions that can be factored.
- Cancel out any common factors in the numerators and denominators.
- Multiply the remaining factors in the numerators and denominators to find the simplified expression.

Let's go through the steps:

- Factor (x^2 - 9) as ((x + 3)(x - 3)).
- Factor (6x + 18) as (6(x + 3)).
- Now, we can rewrite the expression as follows: [ \frac{5x}{(x + 3)(x - 3)} \times \frac{6(x + 3)}{15x^3} ]
- Cancel out any common factors in the numerators and denominators. We can cancel out (x + 3) in the first fraction and (6) in the second fraction: [ \frac{5x}{(x - 3)} \times \frac{x + 3}{5x^3} ]
- Multiply the remaining factors in the numerators and denominators to find the simplified expression: [ \frac{5x(x + 3)}{(x - 3)(5x^3)} ]
- Finally, we can simplify further by canceling out a common factor of (5x) from the numerator and denominator: [ \frac{x + 3}{(x - 3)(x^3)} ]

So, the simplified expression for (\frac{5x}{x^2 - 9} \times \frac{6x + 18}{15x^3}) is (\frac{x + 3}{(x - 3)(x^3)}).

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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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