Question

$$\frac{0.8}{5-0.8}+\frac{0.7}{5-0.7}+\frac{0.5}{5-0.5}; \frac{(0.8)^{2}}{5-0.8}+\frac{(0.7)^{2}}{5-0.7}+\frac{(0.5)^{2}}{5-0.5}+2$$

Answer

$$1.9047619047619+0.16279069767442+0.5/4.5;0.8^2/4.2+0.11395348837209+0.055555555555556+2$$

Solution


Simplify  \(5-0.8\)  to  \(4.2\).
\[\begin{aligned}&\frac{8}{4.2}+\frac{0.7}{5-0.7}+\frac{0.5}{5-0.5}\\&\frac{{0.8}^{2}}{4.2}+\frac{{0.7}^{2}}{5-0.7}+\frac{{0.5}^{2}}{5-0.5}+2\end{aligned}\]
Simplify  \(5-0.7\)  to  \(4.3\).
\[\begin{aligned}&\frac{8}{4.2}+\frac{0.7}{4.3}+\frac{0.5}{5-0.5}\\&\frac{{0.8}^{2}}{4.2}+\frac{{0.7}^{2}}{4.3}+\frac{{0.5}^{2}}{5-0.5}+2\end{aligned}\]
Simplify  \(5-0.5\)  to  \(4.5\).
\[\begin{aligned}&\frac{8}{4.2}+\frac{0.7}{4.3}+\frac{0.5}{4.5}\\&\frac{{0.8}^{2}}{4.2}+\frac{{0.7}^{2}}{4.3}+\frac{{0.5}^{2}}{4.5}+2\end{aligned}\]
Simplify  \({0.7}^{2}\)  to  \(0.49\).
\[\begin{aligned}&\frac{8}{4.2}+\frac{0.7}{4.3}+\frac{0.5}{4.5}\\&\frac{{0.8}^{2}}{4.2}+\frac{0.49}{4.3}+\frac{{0.5}^{2}}{4.5}+2\end{aligned}\]
Simplify  \({0.5}^{2}\)  to  \(0.25\).
\[\begin{aligned}&\frac{8}{4.2}+\frac{0.7}{4.3}+\frac{0.5}{4.5}\\&\frac{{0.8}^{2}}{4.2}+\frac{0.49}{4.3}+\frac{0.25}{4.5}+2\end{aligned}\]
Simplify  \(\frac{8}{4.2}\)  to  \(1.904762\).
\[\begin{aligned}&1.904762+\frac{0.7}{4.3}+\frac{0.5}{4.5}\\&\frac{{0.8}^{2}}{4.2}+\frac{0.49}{4.3}+\frac{0.25}{4.5}+2\end{aligned}\]
Simplify  \(\frac{0.7}{4.3}\)  to  \(0.162791\).
\[\begin{aligned}&1.904762+0.162791+\frac{0.5}{4.5}\\&\frac{{0.8}^{2}}{4.2}+\frac{0.49}{4.3}+\frac{0.25}{4.5}+2\end{aligned}\]
Simplify  \(\frac{0.49}{4.3}\)  to  \(0.113953\).
\[\begin{aligned}&1.904762+0.162791+\frac{0.5}{4.5}\\&\frac{{0.8}^{2}}{4.2}+0.113953+\frac{0.25}{4.5}+2\end{aligned}\]
Simplify  \(\frac{0.25}{4.5}\)  to  \(0.055556\).
\[\begin{aligned}&1.904762+0.162791+\frac{0.5}{4.5}\\&\frac{{0.8}^{2}}{4.2}+0.113953+0.055556+2\end{aligned}\]