Verify the Rational Equation: Is (x²-64)/(x+8) = (x²+64)/(x+8) True?

Is the equation a true or false statement?

$\frac{x^2-64}{x+8}=\frac{x^2+64}{x+8}$

To solve the problem, we first recognize the potential problem in the equation due to the denominator:

• The denominator $x + 8$ implies $x \neq -8$. Otherwise, the expression is undefined.

Next, we will compare the numerators directly:

• Numerator of the left-hand side: $x^2 - 64$
• Numerator of the right-hand side: $x^2 + 64$

The expressions $x^2 - 64$ and $x^2 + 64$ are not equal for any real number $x$, since adding 64 to one is not the same as subtracting 64 from the other. Therefore:

The equation is false for all $x \neq -8$ that are in the domain of the function, as clearly $x^2 - 64 \neq x^2 + 64$.

Thus, the statement is a Lie.