Solve the Function Operation p(x)=x^2+2x , q(x) = square root of 1-x , (q/p)(x) =

$p (x) = x^{2} + 2 x$ , $q (x) = \sqrt{1 - x}$ , $(\frac{q}{p}) (x)$

Step 1

Evaluate $\frac{q}{p}$ .

Replace the function designators in $\frac{q}{p}$ with the actual functions.

$\frac{\sqrt{1 - x}}{x^{2} + 2 x}$

Factor $x$ out of $x^{2} + 2 x$ .

Factor $x$ out of $x^{2}$ .

$\frac{\sqrt{1 - x}}{x \cdot x + 2 x}$

Factor $x$ out of $2 x$ .

$\frac{\sqrt{1 - x}}{x \cdot x + x \cdot 2}$

Factor $x$ out of $x \cdot x + x \cdot 2$ .

$\frac{\sqrt{1 - x}}{x (x + 2)}$

Step 2

Evaluate $\frac{q}{p}$ at $x$ .

$\frac{\sqrt{1 - (x)}}{(x) ((x) + 2)}$

Step 3

Simplify $\frac{\sqrt{1 - (x)}}{(x) ((x) + 2)}$ .

Remove parentheses.

$\frac{\sqrt{1 - (x)}}{(x) ((x) + 2)}$

Remove parentheses.

$\frac{\sqrt{1 - x}}{x (x + 2)}$