QuestionMarch 21, 2026

2) Given the function (x+2)/(x+8)=(1)/(x+2) a) Identify the values of x that cannot be solutions to the equation. b) Find all values of x that make the equation true.

2) Given the function (x+2)/(x+8)=(1)/(x+2) a) Identify the values of x that cannot be solutions to the equation. b) Find all values of x that make the equation true.
2) Given the function (x+2)/(x+8)=(1)/(x+2)
a) Identify the values of x that cannot
be solutions to the equation.
b) Find all values of x that make the
equation true.

Solution
3.0(243 votes)

Answer

a) x = -8,\ -2 ### b) x = -4,\ 1 Explanation 1. Identify restrictions from denominators Denominators are x+8 and x+2. Set each equal to 0: x+8=0 \Rightarrow x=-8, x+2=0 \Rightarrow x=-2. These are excluded values. 2. Solve the equation Start with \frac{x+2}{x+8} = \frac{1}{x+2}. Multiply both sides by (x+8)(x+2) (valid since restrictions handled): (x+2)^2 = x+8 3. Simplify and solve quadratic Expand: x^2 + 4x + 4 = x + 8 Subtract x+8 from both sides: x^2 + 3x - 4 = 0 Factor: (x+4)(x-1)=0 \Rightarrow x=-4 or x=1 4. Check restrictions Neither -4 nor 1 is excluded, so both are valid.

Explanation

1. Identify restrictions from denominators <br /> Denominators are $x+8$ and $x+2$. Set each equal to 0: $x+8=0 \Rightarrow x=-8$, $x+2=0 \Rightarrow x=-2$. These are excluded values. <br />2. Solve the equation <br /> Start with $\frac{x+2}{x+8} = \frac{1}{x+2}$. Multiply both sides by $(x+8)(x+2)$ (valid since restrictions handled): <br /> $(x+2)^2 = x+8$ <br />3. Simplify and solve quadratic <br /> Expand: $x^2 + 4x + 4 = x + 8$ <br /> Subtract $x+8$ from both sides: $x^2 + 3x - 4 = 0$ <br /> Factor: $(x+4)(x-1)=0 \Rightarrow x=-4$ or $x=1$ <br />4. Check restrictions <br /> Neither $-4$ nor $1$ is excluded, so both are valid.
Click to rate:

Similar Questions