Question

Multiply. State any restrictions on the variable. What are the restrictions on the variable? 2. What are the restrictions on the variable? x ≠ ________.B. There are no restrictions on x.

Answer 1

To simplify the equation;

$\frac{x^2-13x+40}{x^2-25}\times\frac{x^2+6x+5}{x^2-7x-8}=1$$\frac{(x-5)(x-8)}{(x-5)(x+5)}\times\frac{(x+5)(x+1)}{(x-8)(x+1)}=1$

Equating the denominators to zero;

$x+5=0\text{ ie x=-5}$$x-8=0\text{ ie x=8}$$\begin{gathered} x-5=0\text{ ie x=5} \\ x+1=0\text{ ie x=-1} \end{gathered}$$Hence,x\ne-1,-5,5,8$