Question

.va rog repede e urgent ​

Answer 1

$\displaystyle a)~\frac{13}{9} +\frac{5}{6} \cdot \frac{8}{3} =\frac{^{2)}13}{9} +\frac{40}{18}=\frac{26+40}{18}=\frac{66^{(6}}{18} }  =\mathbf{\frac{11}{3} }\\ \\ \\ b)~\frac{21}{5} -\frac{1}{10} :\frac{1}{2} =\frac{21}{5} -\frac{1}{10} \cdot 2=\frac{^{2)}21}{5} -\frac{2}{10}=\frac{42-2}{10} =\frac{40}{10} =\mathbf{4}$

$\displaystyle c)~\frac{33}{16}-\frac{5}{16}:\frac{5}{8} -\frac{3}{4} \cdot \frac{3}{4}=\frac{33}{16} -\frac{\not5}{16} \cdot \frac{8}{\not5} -\frac{9}{16}=\frac{33-8-9}{16}=\frac{16}{16}=\mathbf{1}\\\\\\d)~\frac{17}{45}\cdot\frac{15}{34}+\frac{1}{2}+\frac{1}{15} \cdot 5=\frac{1}{3} \cdot \frac{1}{2}+\frac{1}{2}+\frac{5^{(5}}{15}=\frac{1}{6} +\frac{^{3)}1}{2}+\frac{^{2)}1}{3}=\\\\\\=\frac{1+3+2}{6}=\frac{6}{6}=\mathbf{1}$

$\displaystyle e)~\frac{1}{\not2} \cdot \frac{\not2}{3} +\frac{4}{\not5} \cdot \frac{\not5}{6} =\frac{^{2)}1}{3} +\frac{4}{6} =\frac{2+4}{6} =\frac{6}{6}=\mathbf{1} \\ \\\\ f)~\frac{99}{100} :\frac{11}{10} +\frac{17}{40} :\frac{17}{4} =\frac{99}{100} \cdot \frac{10}{11} +\frac{17}{40} \cdot \frac{4}{17} =\frac{^{4)}9}{10} +\frac{4}{40} =\frac{36+4}{40} =\frac{40}{40} =\mathbf{1}$

$\displaystyle g)~\frac{5}{18} +\frac{14}{9} :\frac{7}{3}+\frac{1}{2} :9= \frac{5}{18} +\frac{14}{9} \cdot \frac{3}{7} +\frac{1}{2} \cdot \frac{1}{9} =\frac{5}{18} +\frac{^{6)}2}{3} +\frac{1}{18} =\\ \\ \\=\frac{5+12+1}{18} =\frac{18}{18} =\mathbf{1}\\\\ \\ h)~\frac{^{x)}x}{x+1} +\frac{x}{x^2+x}= \frac{x^2+x}{x^2+x} =\mathbf{1}\\\\ \\ i)~\frac{1}{2a+1} \cdot \frac{4a+2}{3} =\frac{4a+2}{6a+3} =\frac{2(2a+1)}{3(2a+1)} =\mathbf{\frac{2}{3} }$