# How do you simplify (45a^5b(8-a))/(20a^2b^3(a-8)) and what are the restrictions?

May 27, 2015

Given (45a^5b(8-a))/(20a^2b^3(a-8)

This expression is only defined if the denominator is not equal to zero;
therefore $a \ne 0 , b \ne 0 , a \ne 8$

(45a^5b(8-a))/(20a^2b^3(a-8)

$= \textcolor{red}{\frac{45}{20}} \cdot \textcolor{g r e e n}{\frac{{a}^{5}}{{a}^{2}}} \cdot \textcolor{\mathmr{and} a n \ge}{\frac{b}{{b}^{3}}} \cdot \textcolor{b l u e}{\frac{8 - a}{a - 8}}$

$= \textcolor{red}{\frac{9}{4}} \cdot \textcolor{g r e e n}{{a}^{3}} \cdot \textcolor{\mathmr{and} a n \ge}{\frac{1}{{b}^{2}}} \cdot \textcolor{b l u e}{\left(- 1\right)}$

$= - \frac{9 {a}^{3}}{4 {b}^{2}}$