Simplifying, Multiplying and Dividing Rational Expressions

Front

What is a rational expression?

Back

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

Front

What does it mean to simplify a rational expression?

Back

Simplifying a rational expression means to reduce it to its simplest form by canceling common factors in the numerator and denominator.

Front

What is the first step in simplifying a rational expression?

Back

The first step is to factor both the numerator and the denominator completely.

Front

How do you identify restrictions in rational expressions?

Back

Restrictions are values that make the denominator zero. Set the denominator equal to zero and solve for x.

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Back

@@rac{(x-3)(x+3)}{(x-3)(x-3)} = rac{x+3}{x-3}, x e 3@@.

Front

What is the result of multiplying two rational expressions?

Back

To multiply two rational expressions, multiply the numerators together and the denominators together, then simplify.

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Back

@@rac{2(x+6)}{x+2}, x e -2, 0@@.

Front

How do you divide rational expressions?

Back

To divide rational expressions, multiply by the reciprocal of the second expression.

Front

Back

@@rac{(x+10) imes x}{2x imes (x+5)} = rac{x+10}{2(x+5)}, x e -5, 0@@.

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@@rac{(x-1)(x+1)}{(x-2)(x+2)}, x e 2, -2@@.