A) \[\frac{1153}{840}\]
B) \[\frac{128}{105}\]
C) \[\frac{128}{105}\]
D) \[\frac{-125}{256}\]
Correct Answer: A
Solution :
(a): Let \[A=\frac{1}{2}\left[ \frac{-7}{4}+\frac{5}{3}-\frac{5}{6}+\frac{1}{3}-\frac{1}{2} \right]\] \[=\frac{1}{2}\left[ \frac{-21+20-10+4-6}{12} \right]\] \[=\frac{1}{2}\left[ \frac{-13}{12} \right]=\frac{-13}{24}\] Let B\[=\frac{1}{3}\left[ \frac{-12}{5}+\frac{7}{20}-\frac{3}{14}+\frac{1}{7}-\frac{1}{10} \right]\] \[=\frac{1}{3}\left[ \frac{-336-49+30+20-14}{140} \right]\] \[=\frac{1}{3}\left[ \frac{-349}{140} \right]=\frac{-349}{420}\] Now \[A+B=\frac{-13}{24}-\frac{349}{420}\] \[=\frac{-1820-2094}{3360}=\frac{-3904}{3360}\] \[=\frac{-976}{840}=\frac{-122}{105}\].You need to login to perform this action.
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