Question

$$\frac{a}{a+c}\cdot(\frac{a+c}{c}+\frac{a+c}{a})-$$

Answer

$$a^2+c*(2*a+c^2+c*a)-$$

Solution


Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[aa+c(a+{c}^{2}+a+ca)-\]
Collect like terms.
\[aa+c((a+a)+{c}^{2}+ca)-\]
Simplify  \((a+a)+{c}^{2}+ca\)  to  \(2a+{c}^{2}+ca\).
\[aa+c(2a+{c}^{2}+ca)-\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[{a}^{2}+c(2a+{c}^{2}+ca)-\]