question_answer

Add: \[\left( 3{{x}^{2}}-\frac{1}{5}x+\frac{7}{3} \right)+\left( -\frac{1}{4}{{x}^{2}}+\frac{1}{3}x-\frac{1}{6} \right)+\left( -2{{x}^{2}}-\frac{1}{2}x+5 \right)\]

Answer:

\[\left( 3{{x}^{2}}-\frac{1}{5}x+\frac{7}{3} \right)+\left( -\frac{1}{4}{{x}^{2}}+\frac{1}{3}x-\frac{1}{6} \right)\] \[+\left( -2{{x}^{2}}-\frac{1}{2}x+5 \right)\]                                                                                                     \[=3{{x}^{2}}-\frac{1}{4}{{x}^{2}}-2{{x}^{2}}-\frac{1}{5}x+\frac{1}{3}x-\frac{1}{2}x+\frac{7}{3}-\frac{1}{6}+5\] =\[\left( 3-\frac{1}{4}-2 \right){{x}^{2}}+\left( -\frac{1}{5}+\frac{1}{3}-\frac{1}{2} \right)x+\left( \frac{7}{3}-\frac{1}{6}+5 \right)\] \[=\left( \frac{12-1-8}{4} \right){{x}^{2}}+\left( \frac{-6+10-15}{30} \right)x+\left( \frac{14-1+30}{6} \right)\] \[=\frac{3}{4}{{x}^{2}}-\frac{11}{30}x+\frac{43}{6}\]