Simplifying a rational expression

Thread starter Kaylee!
Start date Mar 22, 2009
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Expression Rational Simplifying

In summary, a rational expression is an expression that contains a ratio of two polynomials and can be simplified by factoring both the numerator and denominator completely and then canceling out any common factors. However, it cannot be simplified if the denominator is equal to zero. Simplifying involves rewriting the expression in the simplest form possible, while reducing involves dividing out common factors to create an equivalent expression. There are rules that can assist with simplifying, such as factoring and using the distributive property, but division by zero should be avoided.

Mar 22, 2009

Kaylee!

I've done a calculus problem. The LHS is my answer and the RHS is the answer in the book.

[tex]\frac{2(x-1)^2}{(x^2-1)^2} = \frac{2}{(x+1)^2}[/tex]

What was done to simplify this equation?

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Mar 22, 2009

rock.freak667

Homework Helper

x²-1=(x-1)(x+1)

Mar 22, 2009

Chaos2009

I believe it was called the Difference of Squares. Factor it out and try again.

FAQ: Simplifying a rational expression

What is a rational expression?

A rational expression is an expression that contains a ratio of two polynomials. It can also be referred to as a fractional expression.

How do you simplify a rational expression?

To simplify a rational expression, you need to factor both the numerator and denominator completely. Then, cancel out any common factors and rewrite the remaining terms in the simplest form possible.

Can you simplify a rational expression if the denominator is zero?

No, a rational expression is undefined when the denominator is equal to zero. This is because division by zero is undefined in mathematics.

What is the difference between simplifying and reducing a rational expression?

Simplifying a rational expression means to rewrite it in the simplest form possible, by canceling out common factors. Reducing a rational expression means to divide out any common factors between the numerator and denominator, resulting in an equivalent expression.

Are there any rules for simplifying rational expressions?

Yes, there are a few rules that can help with simplifying rational expressions. These include factoring, canceling out common factors, and using the distributive property. It is also important to remember that division by zero is undefined and should be avoided.