Question

Which shows all the values of x that make the rational expression undefined? x = 6 x = 7 x = –6 or x = 6 x = –7 or x = 7

Answer 1

Explanation:

The rational expression is given by:

$E=\frac{2x^2-72}{5x^2-245} \\ \\ Factor \ out: \\ \\ E=\frac{2(x^2-36)}{5(x^2-49)} \\ \\ E=\frac{2(x-6)(x+36)}{5(x-7)(x+7)} : \ \ \ \ a^2-b^2=(a-b)(a+b)$

The denominator can't be zero, therefore:

$(x-7)(x+7)\neq 0 \\ \\ \\ Thus: \\ \\ \boxed{x\neq 7 \ and x \neq -7}$

Finally, the values of x that make the rational expression undefined are

x = 7 and x = -7