# Simplifying Expressions: \frac{1}{x+2}+\frac{1}{x^2-4}-\frac{2}{x^2-x-2}

• powp
In summary, simplifying expressions is an important skill in mathematics as it allows for easier manipulation and solving of equations, as well as identifying patterns and relationships. To simplify a given expression, find the common denominator and combine fractions. It is also important to check for restrictions on variables to ensure the validity of the simplified expression. Simplifying expressions can also be helpful in solving real-life problems by reducing complex equations to a more manageable form.
powp
Is this correct??

Hello

IS this correct? I have to perform the indicated operations and simplify

$$\frac{1}{x+2}+\frac{1}{x^2-4}-\frac{2}{x^2-x-2}$$

$$\frac{x^2+2x-5}{(x+2)(x-2)(x+1)}$$

Thanks

Shouldn't the numerator of the answer be: $x^2 - 2x - 5$?

Sorry I have made a typing mistake

its

$$\frac{x^2-2x-5}{(x+2)(x-2)(x+1)}$$

is this correct?

Yep, checks out with Mathematica, hehe, I'm so lazy. So yeah it's right.

## 1. What is the purpose of simplifying expressions?

Simplifying expressions is important because it allows us to manipulate and solve equations more easily. It also helps us to find and understand patterns and relationships between different mathematical expressions.

## 2. How can I simplify this particular expression: \frac{1}{x+2}+\frac{1}{x^2-4}-\frac{2}{x^2-x-2}?

To simplify this expression, we can start by finding the common denominator, which in this case is (x+2)(x-2)(x+1). We can then combine the fractions by adding the numerators and keeping the common denominator. After simplifying, the expression becomes \frac{2x+4}{(x+2)(x-2)(x+1)}.

## 3. Can this expression be simplified further?

No, the expression \frac{2x+4}{(x+2)(x-2)(x+1)} is already in its simplest form and cannot be reduced any further.

## 4. Why is it important to check for restrictions when simplifying expressions?

When simplifying expressions, it is important to check for restrictions on the variables involved. This is because certain values of the variables may result in undefined expressions or division by zero, which are not valid in mathematics. By checking for restrictions, we can ensure that our simplified expression is valid for all possible values of the variables.

## 5. Can simplifying expressions help in solving real-life problems?

Yes, simplifying expressions can be very useful in solving real-life problems. In many real-life situations, we encounter complex equations that can be simplified to a more manageable form. This allows us to analyze and solve the problem more easily and efficiently.

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