[Risolto] Es. N. 448

448)

$\frac{1}{3}a-\big(\frac{1}{2}b+\frac{1}{4}b-\frac{3}{5}c\big)+\big(\frac{1}{2}a+\frac{3}{2}b-\frac{1}{2}c\big)-\big(-\frac{1}{6}a-\frac{1}{4}b-\frac{9}{10}c\big)-c$ =

= $\frac{1}{3}a-\frac{1}{2}b-\frac{1}{4}b+\frac{3}{5}c+\frac{1}{2}a+\frac{3}{2}b-\frac{1}{2}c+\frac{1}{6}a+\frac{1}{4}b+\frac{9}{10}c-c$ =

= $\big(\frac{1}{3}+\frac{1}{2}+\frac{1}{6}\big)a+\big(-\frac{1}{2}-\frac{1}{4}+\frac{3}{2}+\frac{1}{4}\big)b+\big(\frac{3}{5}-\frac{1}{2}+\frac{9}{10}-1\big)c$ =

= $\big(\frac{2+3+1}{6}\big)a +\big(\frac{-2-1+6+1}{4}\big)b +\big(\frac{6-5+9-10}{10}\big)c$ =

= $\frac{6}{6}a + \frac{4}{4}b + \frac{0}{10}c$ =

= $a+b$.

1/3·a - (1/2·b + 1/4·b - 3/5·c) + (1/2·a + 3/2·b - 1/2·c) +

- (- 1/6·a - 1/4·b - 9/10·c) - c =

=1/3·a - (3·b/4 - 3·c/5) + (1/2·a + 3/2·b - 1/2·c) +

+(1/6·a + 1/4·b + 9/10·c) - c =

=(1/3 + 1/2 + 1/6)·a + (- 3/4 + 3/2 + 1/4)·b +

+(3/5 - 1/2 + 9/10 - 1)·c =

=a + b + 0 = a + b

N° 448

a/3 - (b/2 + b/4 - 3c/5) + (a/2 + 3b/2 - c/2) - (- a/6 - b/4 - 9c/10) - c =

= a/3 - (3b/4 - 3c/5) + (a/2 + 3b/2 - c/2·c) + (a/6 + b/4 + 9c/10) - c =

= a*(1/3 + 1/2 + 1/6) + b*(- 3/4 + 3/2 + 1/4)+ c*(3/5 - 1/2 + 9/10 - 1) =

= a*1 + b*1 + c*0 = a + b