Question

Solve for x: 5 over quantity x squared minus 4 plus 2 over x equals 2 over quantity x minus 2.

x = 8
x = –4
x = 8 and x = –4
No Solution

Answer 1

`\text{The domain}\\\\x\\eq0\ \wedge\ x\\eq-2\ \wedge\ x\\eq2`

`(5)/(x^2-4)+(2)/(x)=(2)/(x-2)\qquad\text{subtract}\ (2)/(x-2)\ \text{from obth sides}\\\\(5)/(x^2-2^2)+(2)/(x)-(2)/(x-2)=0\\\\(5)/((x-2)(x+2))+(2)/(x)-(2)/(x-2)=0\\\\(5x)/(x(x-2)(x+2))+(2(x-2)(x+2))/(x(x-2)(x+2))-(2x(x+2))/(x(x-2)(x+2))=0\\\\(5x+2(x^2-4)-2x(x+2))/(x(x-2)(x+2))=0\\\\(5x+2x^2-8-2x^2-4x)/(x(x-2)(x+2))=0\\\\(x-8)/(x(x-2)(x+2))=0\iff x-8=0\to\boxed{x=8}\in D`