Solve by Factoring (x^2-16)/(x-4)=x+4

Problem

(x2−16)/(x−4)=x+4

Solution

1. Identify the restriction on the variable by setting the denominator to zero, which gives x≠4

2. Factor the numerator using the difference of squares formula, a2−b2=(a−b)*(a+b)

x2−16=(x−4)*(x+4)

3. Substitute the factored form back into the equation.

((x−4)*(x+4))/(x−4)=x+4

4. Simplify the fraction by canceling the common factor (x−4) provided x≠4

x+4=x+4

5. Analyze the resulting identity, which is true for all values of x except for the restricted value x=4

Final Answer

(x2−16)/(x−4)=x+4⇒x∈ℝ,x≠4

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