1) - 0,25
[tex] \frac{3x - 6}{8x} \times \frac{x}{ {x}^{2} - 4x + 4} = \frac{3(x - 2)}{8(x - 2) {}^{2} } = \frac{3}{8(x - 2)} = \\ = \frac{3}{8(0.5 - 2)} = \frac{3}{8 \times ( - 1.5)} = - \frac{2}{8} = - \frac{1}{4} = - 0.25[/tex]
2) 0,25
[tex](x - 5) {}^{2} + 5(2x - 5) = {x}^{2} - 10x + 25 + 10x - 25 = \\ = {x}^{2} = 0.5 {}^{2} = 0.25[/tex]
3) 1,5
[tex] \frac{ {x}^{3} + 1}{ {x}^{2} - x + 1 } = \frac{(x + 1)( {x}^{2} - x + 1)}{ {x}^{2} - x + 1} = x + 1 = 0.5 + 1 = 1.5[/tex]
4) - 2,5
[tex] \frac{ {x}^{2} -9 }{3 + x} = \frac{(x - 3)(x + 3)}{3 + x} = x - 3 = 0.5 - 3 = - 2.5[/tex]
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Answers & Comments
1) - 0,25
[tex] \frac{3x - 6}{8x} \times \frac{x}{ {x}^{2} - 4x + 4} = \frac{3(x - 2)}{8(x - 2) {}^{2} } = \frac{3}{8(x - 2)} = \\ = \frac{3}{8(0.5 - 2)} = \frac{3}{8 \times ( - 1.5)} = - \frac{2}{8} = - \frac{1}{4} = - 0.25[/tex]
2) 0,25
[tex](x - 5) {}^{2} + 5(2x - 5) = {x}^{2} - 10x + 25 + 10x - 25 = \\ = {x}^{2} = 0.5 {}^{2} = 0.25[/tex]
3) 1,5
[tex] \frac{ {x}^{3} + 1}{ {x}^{2} - x + 1 } = \frac{(x + 1)( {x}^{2} - x + 1)}{ {x}^{2} - x + 1} = x + 1 = 0.5 + 1 = 1.5[/tex]
4) - 2,5
[tex] \frac{ {x}^{2} -9 }{3 + x} = \frac{(x - 3)(x + 3)}{3 + x} = x - 3 = 0.5 - 3 = - 2.5[/tex]