Exercise 1 Page 693

Consider the given rational expression. 8/x^2-16 To identify the excluded values, we need to remember that the denominator cannot be equal to 0 because division by 0 is not defined. This means we need exclude the values of x that would make the denominator equal to 0. x^2-16=0 One way of solving such quadratic equations is through factoring. We can use the Difference of Squares Formula for that.

x^2-16=0

WritePow

Write as a power

x^2-4^2=0

FacDiffSquares

a^2-b^2=(a+b)(a-b)

(x+4)(x-4)=0

Once the expression is written in factored form, we can apply the Zero Product Property to find the solutions to the equation.

(x+4)(x-4)=0

ZeroProdProp

Use the Zero Product Property

lcx+4=0 & (I) x-4=0 & (II)

SubEqn

(I): LHS-4=RHS-4

lx=- 4 x-4=0

AddEqn

(II): LHS+4=RHS+4

lx=- 4 x=4

These two values make the denominator equal to 0. Therefore, the excluded values are - 4 and 4.