Explanation Given Information: The given fraction is x 2 − x − 2 2 x 2 − 8 ⋅ 18 − 2 x 2 x 2 − 5 x + 4 ⋅ x 2 − 2 x − 8 x 2 − 6 x + 9 . Formula used: The difference of two squares: x 2 − a 2 = ( x + a ) ( x − a ) Calculation: To solve the given fraction, there is a need to find the factors of numerator and denominator. The factored form of numerator terms are x 2 − x − 2 = ( x − 2 ) ( x + 1 ) x 2 − 2 x − 8 = ( x − 4 ) ( x + 2 ) and 18 − 2 x 2 = 2 ( 9 − x 2 ) Where ( 9 − x 2 ) can be factored using the difference of two squares into ( 3 + x ) ( 3 − x ) . Similarly, the factored form of denominator is x 2 − 5 x + 4 = ( x − 4 ) ( x − 1 ) x 2 − 6 x + 9 = ( x − 3 ) 2 2 x 2 − 8 = 2 ( x 2 − 4 ) Where ( x 2 − 4 ) = ( x + 2 ) ( x − 2 )

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Chapter 0.7, Problem 13E

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To calculate: The simplified form of the expression x2−x−22x2−8⋅18−2x2x2−5x+4⋅x2−2x−8x2−6x+9 by performing the indicated operations.

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Chapter 0.7, Problem 12E

Chapter 0.7, Problem 14E

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The simplified form of the expression x 2 − x − 2 2 x 2 − 8 ⋅ 18 − 2 x 2 x 2 − 5 x + 4 ⋅ x 2 − 2 x − 8 x 2 − 6 x + 9 by performing the indicated operations.

Solution Summary: The author explains that to solve the given tion, there is a need to find the factors of numerator and denominator.

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To calculate: The simplified form of the expression x2−x−22x2−8⋅18−2x2x2−5x+4⋅x2−2x−8x2−6x+9 by performing the indicated operations.

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