Simplify rational expressions

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What is a rational expression?

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

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CCSS.HSA.APR.D.7

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How do you simplify a rational expression?

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

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CCSS.HSA.APR.D.6

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The first step is to find a common denominator for the two fractions.

Tags

CCSS.HSA.APR.D.7

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What is the factored form of the polynomial x^2 - 4x - 32?

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The factored form is (x - 8)(x + 4).

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What does it mean to factor a polynomial?

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Factoring a polynomial means expressing it as a product of its factors, which are polynomials of lower degrees.

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Tags

CCSS.HSA.APR.D.6

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

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

Tags

CCSS.HSA.APR.D.6

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How do you factor the expression k^2 - 2k - 24?

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To factor k^2 - 2k - 24, look for two numbers that multiply to -24 and add to -2, which are 4 and -6. Thus, it factors to (k + 4)(k - 6).

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The result is 6.

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CCSS.HSA.APR.D.7

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What is the process of adding two rational expressions?

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To add two rational expressions, find a common denominator, rewrite each expression with that denominator, and then combine the numerators.

Tags

CCSS.HSA.APR.D.7