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| − | Vi förenklar först uttryckets första term:
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| − | <math> {2\,x^2 - x^3 \over 2\,x^2 - 8} \; = \; {x^2\,(2 - x) \over 2\,(x^2 - 4)} \; = \; {x^2\,(2 - x) \over 2\,(x-2)\cdot(x+2)} \; = \; </math>
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| − | <math> = \; {-\,x^2\,(x - 2) \over 2\,(x-2)\cdot(x+2)} \; = \; {-\,x^2 \over 2\,(x+2)} </math> Detta sätts in i hela uttrycket:
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| − | <math> {2\,x^2 - x^3 \over 2\,x^2 - 8} - {x \over x+2} + {x+2 \over 2} \; = \; {-\,x^2 \over 2\,(x+2)} - {x \over x+2} + {x+2 \over 2} \; = \; </math>
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| − | <math> = \; {-\,x^2 \over 2\,(x+2)} - {2\cdot x \over 2\cdot(x+2)} + {(x+2)\cdot(x+2) \over 2\cdot(x+2)} \; = \; </math>
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| − | <math> = \; {-\,x^2 - 2\,x + (x+2)^2 \over 2\,(x+2)} \; = \; {-\,x^2 - 2\,x + x^2 + 4\,x +4 \over 2\,(x+2)} \; = \; </math>
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| − | <math> = \; {-2\,x + 4\,x + 4 \over 2\,(x+2)} \; = {2\,x + 4 \over 2\,(x+2)} \; = \; {2\,(x+2) \over 2\,(x+2)} \; = \; 1 </math>
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