Simplifying Rational Expressions

Front

What is a rational expression?

Back

A rational expression is a fraction where the numerator and the denominator are both polynomials.

Front

How do you simplify a rational expression?

Back

To simplify a rational expression, factor both the numerator and the denominator and then cancel any common factors.

Front

What is the difference between a proper and improper rational expression?

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A proper rational expression has a degree of the numerator less than the degree of the denominator, while an improper rational expression has a degree of the numerator greater than or equal to the degree of the denominator.

Front

What does it mean for a rational expression to be undefined?

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A rational expression is undefined when its denominator equals zero.

Front

How can you determine the values that make a rational expression undefined?

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Set the denominator equal to zero and solve for the variable.

Front

What is the sum of cubes formula?

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The sum of cubes formula is a^3 + b^3 = (a + b)(a^2 - ab + b^2).

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What is the difference of cubes formula?

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The difference of cubes formula is a^3 - b^3 = (a - b)(a^2 + ab + b^2).

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What is factoring in the context of algebra?

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Factoring is the process of breaking down an expression into simpler components, or factors, that when multiplied together give the original expression.

Front

What is the first step in simplifying the expression (x + 6)/(x - 5)?

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The first step is to check if the numerator and denominator can be factored further.

Front

What is the significance of identifying common factors in rational expressions?

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Identifying common factors allows you to simplify the expression, making calculations easier.