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1. Explain why the equation x+1/x-3  = 4/x-3 has no solution.

2 What are the domain restrictions for the following expression: 2x-8 / x^2-6x+8  and why are these values restrictions?

Oct 18, 2018

#1
+5038
+1

$$x+1 = 4 \Rightarrow x=3\\ \text{however 3 is not in the domain of either side of the equation (no division by 0)}$$

$$\text{again the point is no dividing by 0}\\ x^2-6x+8 = (x-4)(x-2) = 0 \text{ when }x=4, \text{ or }x=2\\ \text{Thus neither 4 nor 2 are included in the domain}$$

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Oct 18, 2018

#1
+5038
+1
$$x+1 = 4 \Rightarrow x=3\\ \text{however 3 is not in the domain of either side of the equation (no division by 0)}$$
$$\text{again the point is no dividing by 0}\\ x^2-6x+8 = (x-4)(x-2) = 0 \text{ when }x=4, \text{ or }x=2\\ \text{Thus neither 4 nor 2 are included in the domain}$$