Question

Tomando x=13/20, y=7/15 e z=2/7, calcule a seguinte expressão:


−2+3
2+3−2

Answer 1

$\frac{x-2y+3z}{2x+3y-2z}$

= $\frac{ \frac{13}{20}-2. \frac{7}{15}+2. \frac{2}{7} }{2. \frac{13}{20}+3. \frac{7}{15} -2. \frac{2}{7} }$

= $\frac{ \frac{13}{20}- \frac{14}{15}+ \frac{6}{7} }{ \frac{26}{20}+ \frac{21}{15}- \frac{4}{7} }$

Fazemos o M.M.C de 7   15    20

7    15    20  | 2
7    15    10  | 2
7    15     5   | 3
7    15     5   | 3
7     5      5   | 5
7    1       1   | 7
1    1       1

M.M.C de 7, 15 e 20 = 2.2.3.5.7 = 420

= $\frac{ \frac{420}{20}.13- \frac{420}{15}.14+ \frac{420}{7}.6 }{ \frac{420}{20}.26+ \frac{420}{15}.21- \frac{420}{7}.4 }$

= $\frac{ \frac{273-392+360}{420} }{ \frac{546+588-240}{420} }$

= $\frac{ \frac{241}{420} }{ \frac{894}{420} }$

= $\frac{241}{420}. \frac{420}{894}$

= $\frac{241}{894}$