# Preform the operations and simplifying

• powp
In summary, the conversation involves someone seeking help with simplifying and performing operations on a mathematical expression. They provide their current progress and ask for confirmation and guidance on what to do next. They also encounter a small mistake and seek clarification on a term used by the expert summarizer. The expert states that the expression can be factored using specific variables, but it depends on the purpose of the simplification.
powp
Hello

I have to preform the operations and simplifying it.

This is what i have

$$\frac{1}{x}+\frac{1}{x-2}+\frac{3}{(x-2)^2}$$

$$=\frac{3x^2-7x+8}{x(x-2)(x-2)}$$

Is this correct?? Where do I go from here?

Thanks

P

$$\frac{1}{x}+\frac{1}{x-2}+\frac{3}{(x-2)^2}$$

$$\frac{(x-2)^2}{x(x-2)^2} + \frac{x(x-2)}{x(x-2)^2} + \frac{3x}{x(x-2)^2}$$

$$\frac{3x+(x-2)x+(x-2)^2}{(x-2)^2}$$

The top can be 'factored' taking a = 1, b = x, c = 3x and y = (x-2)

I made a mistake when typing the question.

$$\frac{2}{x}+\frac{1}{x-2}+\frac{3}{(x-2)^2}$$

what do you mean by "The top can be 'factored' taking a = 1, b = x, c = 3x and y = (x-2)"??

$$\frac{3x+(x-2)x+2(x-2)^2}{(x-2)^2}$$

$$3x+(x-2)x+2(x-2)^2$$ can be factored if you want it to be, but it depends on what your trying to do.

## 1. What are the basic operations in simplifying expressions?

The basic operations in simplifying expressions are addition, subtraction, multiplication, and division. These operations are used to combine like terms, remove parentheses, and simplify fractions in an expression.

## 2. How do I simplify expressions with exponents?

To simplify expressions with exponents, you can use the rules of exponents which state that when multiplying terms with the same base, you add the exponents and when dividing terms with the same base, you subtract the exponents.

## 3. Can I combine terms with different variables when simplifying expressions?

No, when simplifying expressions, you can only combine terms with the same variables. This means that you cannot combine terms with x and y, but you can combine terms with 2x and 3x.

## 4. How do I simplify expressions with parentheses?

To simplify expressions with parentheses, you must use the distributive property. This means that you must multiply the number outside the parentheses by each term inside the parentheses.

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

The purpose of simplifying expressions is to make them easier to read and understand. It also allows you to solve equations and problems more efficiently by reducing the number of terms and operations in an expression.

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