Q : 27 - Intermediate Algebra

Question

Simplify the rational expression $\frac{z^2-9z+20}{16-z^2}$

Step-by-Step Solution

Answer

The simplified form of rational expression $\frac{z^2-9z+20}{16-z^2} is \frac{-(z-5)}{(z+4)} ,z\ne -4$.

Step 1: Given information

Given rational expression is $\frac{z^2-9z+20}{16-z^2}$

We have to simplify the given rational expression 

Step 2 : Simplification of the rational expression

Here rational expression is  $\frac{z^2-9z+20}{16-z^2}$.For simplification we need to factor both numerator and denominator separately  and find out the common factors,  we get $\frac{z^2-9z+20}{16-z^2}=\frac{(z-4)(z-5)}{(4-z)(4+z)}$. We can see that factors are that are opposite hence an expression and its opposite divide to −1.Then rational becomes $$\begin{gathered} \frac{z^2-9z+20}{16-z^2}=\frac{(z-4)(z-5)}{(4-z)(4+z)} \\ =(-1)\frac{(z-4)(z-5)}{(z+4)(z-4)} \\ =\frac{-(z-5)}{ (z+4)} ,z\ne -4\sin ce (z-4) is the common factors so divide out \end{gathered}$$