a: \(\dfrac{6x^3-7x^2-x+2}{2x+1}\)
\(=\dfrac{6x^3+3x^2-10x^2-5x+4x+2}{2x+1}\)
\(=\dfrac{3x^2\left(2x+1\right)-5x\left(2x+1\right)+2\left(2x+1\right)}{2x+1}=3x^2-5x+2\)
b: \(\dfrac{x^2-y^2+6x+9}{x+3+y}\)
\(=\dfrac{\left(x^2+6x+9\right)-y^2}{x+3+y}\)
\(=\dfrac{\left(x+3\right)^2-y^2}{x+3+y}=\left(x+3\right)-y\)
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a) (6x³ - 7x² - x + 2) : (2x + 1)
= (6x³ + 3x² - 10x² - 5x + 4x + 2) : (2x + 1)
= [(6x³ + 3x²) - (10x² + 5x) + (4x + 2)] : (2x + 1)
= [3x²(2x + 1) - 5x(2x + 1) + 2(2x + 1)] : (2x + 1)
= (2x + 1)(3x² - 5x + 2) : (2x + 1)
= 3x² - 5x + 2
b) (x² - y² + 6x + 9) : (x + 3 + y)
= [(x² + 6x + 9) - y²] : (x + 3 + y)
= [(x + 3)² - y²] : (x + 3 + y)
= (x + 3 - y)(x + 3 + y) : (x + 3 + y)
= x + 3 - y
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