Explanation Calculation: The given expression is 2 x 2 + 3 x − 2 2 + 3 x − 2 x 2 ÷ 5 x + 10 4 x + 2 . Simplify the expression as follows. 2 x 2 + 3 x − 2 2 + 3 x − 2 x 2 ÷ 5 x + 10 4 x + 2 = 2 x 2 + 3 x − 2 − ( 2 x 2 − 3 x − 2 ) × 4 x + 2 5 x + 10 = 2 x 2 + 4 x − x − 2 − ( 2 x 2 + x − 4 x − 2 ) × 2 ( 2 x + 1 ) 5 ( x + 2 ) = 2 x ( x + 2 ) − 1 ( x + 2 ) − ( x ( 2 x + 1 ) − 2 ( 2 x + 1 ) ) × 2 ( 2 x + 1 ) 5 ( x + 2 ) = ( 2 x − 1 ) ( x + 2 ) − ( ( 2 x + 1 ) ( x − 2 ) ) × 2 ( 2 x + 1 ) 5 ( x + 2 ) = 2 ( 2 x − 1 ) 5 ( x − 2 ) , where x ≠ − 1 2 , ± 2 5 2 Check the answer with a calculator as follows

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Chapter 6.5, Problem 41E

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To simplify: The expression 2x2+3x−22+3x−2x2÷5x+104x+2 and check the answer with a calculator.

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Chapter 6.5, Problem 40E

Chapter 6.5, Problem 42E

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The expression 2 x 2 + 3 x − 2 2 + 3 x − 2 x 2 ÷ 5 x + 10 4 x + 2 and check the answer with a calculator.

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To simplify: The expression 2x2+3x−22+3x−2x2÷5x+104x+2 and check the answer with a calculator.

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