question_answer 25)

Verify that \[a\div (b+c)\ne (a\div b)+(a\div b)\]\[+\]\[(a\div c)\]for each of the following values of a, b and c (a) \[a=12,b=-4,c=2\]            (b) \[a=(-10),b=1,c=1\]                

Answer:

                (a)\[~a\div (b+c)=12\div [(-4)+2]=12\div \left( -2 \right)=-6\] \[(a\div b)+(a\div c)=12\div (-4)+12\div 2=-3+6=3\] So, \[a\div (b+c)\ne (a\div b)+(a\div c)\] (b) \[a\div (b+c)=(-10)\div (1+1)=(-10)\div 2=-5\] \[a\div b+a\div c=(-10)\div 1+(-10)\div 1\] \[=\left( -10 \right)+\left( -10 \right)=-20\] So, \[a\div (b+c)\ne (a\div b)+(a\div c)\].