\(\dfrac{254x399-145}{254+399x254}\)
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a) \(=\dfrac{254x\left(400-1\right)-145}{254+\left(400-1\right)x253}=\dfrac{254x400-254-145}{254+253x400-253}\)
\(=\dfrac{101600-399}{101200+1}=\dfrac{101211}{101201}=\dfrac{101201+10}{101201}=1+\dfrac{10}{101201}\)
b) \(=\dfrac{5392+\left(600+1\right)x5391}{5392x\left(600+1\right)-69}=\dfrac{5392+600x5391+5391}{5392x600+5392-69}\)
\(=\dfrac{10783+3234600}{3235200+5323}=\dfrac{\text{3245383}}{\text{3240523}}=\dfrac{3240523+60}{3240523}=1+\dfrac{60}{3240523}\)
c) \(=\dfrac{1}{2}x\left(\dfrac{1}{2}-\dfrac{1}{4}\right)+\dfrac{1}{2}x\left(\dfrac{1}{4}-\dfrac{1}{8}\right)+\dfrac{1}{32}\)
\(=\dfrac{1}{2}x\left(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{8}\right)+\dfrac{1}{32}\)
\(=\dfrac{1}{2}x\left(\dfrac{1}{2}-\dfrac{1}{8}\right)+\dfrac{1}{32}=\dfrac{3}{16}+\dfrac{1}{32}=\dfrac{7}{32}\)
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254 x 399 - 145/254 + 339 x 253
= 101346 - 145/254 + 85767
= 187112,4291
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\(\frac{254\cdot399-145}{254+399\cdot253}=\frac{\left(253+1\right)\cdot399-145}{254+399\cdot253}\)
\(=\frac{253\cdot399+399-145}{254+399\cdot253}\)
\(=\frac{253\cdot399+254}{254+399\cdot253}\)
\(=1\)
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A = \(\dfrac{254\times399-145}{254+399\times253}\)
A = \(\dfrac{\left(253+1\right)\times399-145}{254+399\times253}\)
A = \(\dfrac{253\times399+399-145}{254+399\times253}\)
A = \(\dfrac{253\times399+254}{254+399\times253}\)
A = 1
a) \(254x399-145=\left(250+4\right)\left(400-1\right)-145\)
\(=100000+1600-250-145-4=101600-\left(250+145+4\right)\)
\(=101600-399=101201\)
b) \(254+399x253=254+\left(400-1\right)x\left(250+3\right)\)
\(=254+100000+1200-250-3\)
\(=101454-250-3=101201\)
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a, \(\dfrac{254\times399-145}{254+399\times253}\)
= \(\dfrac{\left(253+1\right)\times399-`45}{254+399\times253}\)
= \(\dfrac{253\times399+399-145}{253\times399+254}\)
= \(\dfrac{253\times399+254}{253\times399+254}\)
= 1
b, \(\dfrac{5932+6001\times5931}{5932\times6001-69}\)
= \(\dfrac{5932+6001\times5931}{\left(5931+1\right)\times6001-69}\)
= \(\dfrac{5932+6001\times5931}{5931\times6001+6001-69}\)
= \(\dfrac{5932+6001\times5931}{5931\times6001+5932}\)
= 1
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\(\frac{254.399-145}{254+399.253}=\frac{253.399+399-145}{253.399+254}=\frac{253.399+254}{253.399+254}=1\)
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\(\frac{254+399.253}{254.399-145}=\frac{254+399.253}{\left(253+1\right).399-145}=\frac{254+399.253}{253.399+\left(399-145\right)}\)
\(=\frac{399.253+254}{399.353+354}=1\)
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\(\frac{254.399-145}{254+399.253}=\frac{\left(253+1\right).399-145}{254+399.253}=\frac{253.399+\left(399-145\right)}{254+399.253}\)
\(=\frac{253.399+254}{254+399.253}=1\)
\(\frac{254\times399-145}{254+399\times253}\)
\(=\frac{253\times399+399-145}{254+399\times253}\)
\(=\frac{253\times399+254}{254+399\times253}\)
\(=1\)
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\(\frac{254.399-145}{254+399.253}\)
\(=\frac{253.399+399-145}{254+399.253}\)
\(=\frac{253.399+254}{254+399.253}=1\)