TINH NHANH : \(\frac{2004\times2007+6}{2005\times2005+2009}=?\)
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\(\frac{2005\cdot2004-1}{2003\cdot2005+2004}\)
\(=\frac{2005\cdot\left(2003+1\right)-1}{2003\cdot2005+2004}\)
\(=\frac{2005\cdot2003+2005-1}{2003\cdot2005+2004}\)
\(=\frac{2005\cdot2003+2004}{2003\cdot2005+2004}\)
\(=1\)
2005 x 2004 - 1 / 2003 × 2005 + 2004
= 2005 × (2003 + 1) - 1 / 2003 × 2005 + 2004
= 2005 × 2003 + (2005 - 1) / 2003 × 2005 + 2004
= 2005 × 2003 + 2004 / 2003 × 2005 + 2004
= 1
\(\frac{2005x2004-1}{2003x2005+2004}\)=\(\frac{4018019}{4018019}\)= 1
\(=\frac{2005\times\left(2006+1\right)-1}{2004+2005\times2006}=\frac{2005\times2006+2005\times1-1}{2004+2005\times2006}=\frac{2005\times2006+2004}{2004+2005\times2006}=1\)
\(\dfrac{2004\cdot2007+6}{2005\cdot2005+2009}=\dfrac{2004\cdot2005+2004\cdot2+6}{2005\cdot2004+2005+2009}\\ =\dfrac{2004\cdot2005+4014}{2004\cdot2005+4014}=1\)
\(\frac{2005\times2004-1}{2003\times2005+2004}=\frac{2005\times2003+2005-1}{2003\times2005+2004}=\frac{2005\times2003+2004}{2003\times2005+2004}=1\)
Tham khảo
Ta có:
2004×2007+6
=(2005-1)×2007+6
=2005×2007-2007+6
=2005×(2005+2)-2007+6
=2005×2005+2005×2-2007+6
=2005×2005+4010-2007+6
=2005×2005+9
Vậy 2004×2007+6/2005×2005+2009=1
Ta có: \(\frac{2004\cdot2007+6}{2005\cdot2005+2009}=\frac{\left(2005-1\right)\cdot2007+6}{2005\cdot2005+2009}=\frac{2005\cdot2007-1\cdot2007+6}{2005\cdot2005+2009}=\frac{2005\cdot2007-2007+6}{2005\cdot2005+2009}\)
\(=\frac{\text{2005 x (2005 + 2) - 2007 + 6}}{\text{2005 x 2005 + 2009}}=\frac{\text{2005 x 2005 + 2005 x 2 - 2007 + 6}}{\text{2005 x 2005 + 2009}}=\frac{\text{2005 x 2005 + 4010 - 2007 + 6}}{\text{2005 x 2005 + 2009}}=\text{ }\frac{\text{2005 x 2005 + 2009}}{\text{2005 x 2005 + 2009}}=1\)