Question

simplifique a expressão

Answer 1

Olá, bom dia!

Temos a seguinte expressão:

B) 

$\\ \frac{ (\frac{5}{6} )^2+2* \frac{(1}{18})* (\frac{1}{6} )- (\frac{2}{5})^2 }{ \sqrt{( \frac{3}{5} }+ \frac{4}{3} )^2} \\ \\ \frac{ \frac{5*5}{6*6} + \frac{2*1*1}{18*6} - \frac{2*2}{5*5} }{ \sqrt{ (\frac{3*3+5*4}{5*3} )^2} } \\ \\ \frac{ \frac{25}{36}+ \frac{2}{108} - \frac{4}{25} }{ \sqrt{( \frac{9+20}{15} )^2} } \\ \\ \frac{ \frac{25}{36}+ \frac{1}{54} - \frac{4}{25} }{ \sqrt{ (\frac{29}{15} )^2} }$

Poderíamos ter cortado a raiz com a potencia de "2" desde o inicio. mas vamos cancelar agora.

$\\ \frac{ \frac{25}{36}+ \frac{1}{54} - \frac{4}{25} }{ \frac{29}{15} }$

Tirando mmc entre 36, 54  e 25:

25, 36, 54 | 2

25 , 18, 27 | 2

25 , 9 , 27 | 3

25 , 3, 9 | 3

25, 1, 3 | 3

25, 1, 1, | 5

5, 1, 1, | 5

1, 1, 1 | 1

mmc = 1*5*5*3*3*3*2*2 → 2700


$\\ =\frac{ \frac{75*25+50*1-108*4}{2700} }{ \frac{29}{15} } \\ \\ = \frac{ \frac{1875+50-432}{2700} }{ \frac{29}{15} } \\ \\ = \frac{1493}{2700} * \frac{15}{29} \\ \\ = \frac{1493*15}{2700*29} \\ \\ = \frac{22.395}{78.300} \\ \\ = \frac{4479}{15.660} \\ \\ = \frac{1493}{5220} \\ \\ =$

Answer 2

Resposta:

$\textsf{Segue a resposta abaixo}$

Explicação passo-a-passo:

$\mathsf{\left(\dfrac{\dfrac{25}{36}+\diagup\!\!\!\!2\cdot\left(\dfrac{1}{\diagup\!\!\!\!2\cdot9}\right)\cdot\left(\dfrac{1}{6}\right)-\dfrac{4}{25}}{\sqrt{\left(\dfrac{(3\cdot3)+(4\cdot5)}{5\cdot3}\right)^2}}\right)=\left(\dfrac{\dfrac{25}{36}+\dfrac{1}{9}\cdot\left(\dfrac{1}{6}\right)-\dfrac{4}{25}}{\sqrt{\left(\dfrac{29}{15}\right)^2}}\right)}$

$\mathsf{\left(\dfrac{\dfrac{25}{36}+\dfrac{1}{54}-\dfrac{4}{25}}{\dfrac{29}{15}}\right)=\left(\dfrac{\dfrac{(25\cdot3)+2}{2\cdot(18\cdot3)}-\dfrac{4}{25}}{\dfrac{29}{15}}\right)}$

$\mathsf{\left(\dfrac{\dfrac{77}{108}-\dfrac{4}{25}}{\dfrac{29}{15}}\right)=\left(\dfrac{\dfrac{(77\cdot25)-(4\cdot108)}{108\cdot25}}{\dfrac{29}{15}}\right)}$

$\mathsf{\left(\dfrac{\dfrac{1493}{2700}}{\dfrac{29}{15}}\right)=\left(\dfrac{1493}{180\cdot~\!\diagup\!\!\!\!\!\!{15}}\right)\cdot\left(\dfrac{~\!\diagup\!\!\!\!\!\!{15}}{29}\right)}$

$\boxed{\boxed{\mathsf{\left(\dfrac{\left(\dfrac{5}{6}\right)^2+2\cdot\left(\dfrac{1}{18}\right)\cdot\left(\dfrac{1}{6}\right)-\left(\dfrac{2}{5}\right)^2}{\sqrt{\left(\dfrac{3}{5}+\dfrac{4}{3}\right)^2}}\right)=\dfrac{1493}{5220}}}}$