Wykonaj działania:
a) ([1:a+b]+[1:a-b]) * (1- [a+b :2a])
b) 1- ([a-1] : [a-2])
a)
b)
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a)![([\frac{1}{a}+b]+[\frac{1}{a}-b])*(1-[a+b:\frac{2}{a}]) = (\frac{2}{a})*(1-a+\frac{ab}{2}) =\frac{2}{a} -2+b = \frac{2}{a} * (-\frac{1}{2})+b = -\frac{1}{a}+b ([\frac{1}{a}+b]+[\frac{1}{a}-b])*(1-[a+b:\frac{2}{a}]) = (\frac{2}{a})*(1-a+\frac{ab}{2}) =\frac{2}{a} -2+b = \frac{2}{a} * (-\frac{1}{2})+b = -\frac{1}{a}+b](https://tex.z-dn.net/?f=%28%5B%5Cfrac%7B1%7D%7Ba%7D%2Bb%5D%2B%5B%5Cfrac%7B1%7D%7Ba%7D-b%5D%29%2A%281-%5Ba%2Bb%3A%5Cfrac%7B2%7D%7Ba%7D%5D%29+%3D+%28%5Cfrac%7B2%7D%7Ba%7D%29%2A%281-a%2B%5Cfrac%7Bab%7D%7B2%7D%29+%3D%5Cfrac%7B2%7D%7Ba%7D+-2%2Bb+%3D++%5Cfrac%7B2%7D%7Ba%7D+%2A+%28-%5Cfrac%7B1%7D%7B2%7D%29%2Bb+%3D+-%5Cfrac%7B1%7D%7Ba%7D%2Bb)
b)![1-([a-1]:[a-2]) = 1-(\frac{a}{1}-1)*(\frac{1}{a}-\frac{1}{2}) = 1-(1-\frac{a}{2}-\frac{1}{a}+\frac{1}{2}) = 1-1+\frac{a}{2}+\frac{1}{a}-\frac{1}{2} = \frac{a}{2}+\frac{1}{a}-\frac{1}{2} 1-([a-1]:[a-2]) = 1-(\frac{a}{1}-1)*(\frac{1}{a}-\frac{1}{2}) = 1-(1-\frac{a}{2}-\frac{1}{a}+\frac{1}{2}) = 1-1+\frac{a}{2}+\frac{1}{a}-\frac{1}{2} = \frac{a}{2}+\frac{1}{a}-\frac{1}{2}](https://tex.z-dn.net/?f=1-%28%5Ba-1%5D%3A%5Ba-2%5D%29+%3D+1-%28%5Cfrac%7Ba%7D%7B1%7D-1%29%2A%28%5Cfrac%7B1%7D%7Ba%7D-%5Cfrac%7B1%7D%7B2%7D%29+%3D+1-%281-%5Cfrac%7Ba%7D%7B2%7D-%5Cfrac%7B1%7D%7Ba%7D%2B%5Cfrac%7B1%7D%7B2%7D%29+%3D+1-1%2B%5Cfrac%7Ba%7D%7B2%7D%2B%5Cfrac%7B1%7D%7Ba%7D-%5Cfrac%7B1%7D%7B2%7D+%3D+%5Cfrac%7Ba%7D%7B2%7D%2B%5Cfrac%7B1%7D%7Ba%7D-%5Cfrac%7B1%7D%7B2%7D)