Question

1998 x 1996 + 1997 x 11 + 1985 / 1997 x 1996 - 1995 x 1996

 

Answer 1

\(=\dfrac{1997^2-1+1997\cdot11+1997-12}{1997^2-1997-\left(1997-2\right)\left(1997-1\right)}\)

\(=\dfrac{1997^2+12\cdot1997-13}{1997^2-1997-\left(1997^2-3\cdot1997+2\right)}\)

\(=\dfrac{\left(1997+13\right)\left(1997-1\right)}{1997^2-1997-1997^2+3\cdot1997-2}\)

\(=\dfrac{1996\cdot2010}{2\left(1997-1\right)}=\dfrac{2010}{2}=1005\)