Simplifying Rational Expressions

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What is a rational expression?

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

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What does it mean to simplify a rational expression?

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To simplify a rational expression means to reduce it to its simplest form by factoring and canceling common factors.

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The first step is to factor out any common terms in the numerator and denominator.

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x must be excluded for values 2 and -5 to prevent division by zero.

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How do you factor the expression 3x^2 + 18x + 15?

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First, factor out the greatest common factor (GCF), which is 3, resulting in 3(x^2 + 6x + 5). Then factor the quadratic to get 3(x + 5)(x + 1).

Front

What is the GCF of the expression 3x^2 + 18x + 15?

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The GCF is 3.

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What is the difference between a polynomial and a rational expression?

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A polynomial is an expression made up of variables and coefficients, while a rational expression is a fraction where both the numerator and denominator are polynomials.

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What is the importance of factoring in simplifying rational expressions?

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Factoring allows us to identify and cancel common factors in the numerator and denominator, simplifying the expression.

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What does it mean for an expression to be in its simplest form?

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An expression is in its simplest form when it cannot be reduced any further, meaning there are no common factors left to cancel.