Rational expression questions

Question

Rational expression being referenced: ((1/6+3)+(6/x^2+4x+3))*(x+3)/(x+1). Simplified version: (x+7)/(x+1)^2

Questions I need help with:

1.) Are there any values x cannot be? Explain.

2.) Find the values of x that make the expression equal to 0. Explain the steps you used to find these values.

Answer 1

If an equation with 0 as a denominator is a result of using "x"; that "x" can't be used.

Answer 2

1) you cannot divide by zero, so x cannot be -1.

2) Finding values of x to make the expression 0.

Starting from the simplified form the the expression:

(x+7)/(x+1)^2 = 0

multiply both sides by (x+1)^2:

(x+7) = 0 * (x+1)^2

simplify:

x+7 =0

solution:

x=-7