Question

solve the following rational equation.

\\\frac{5}{x - 6} = \frac{x + 6}{x}\\

\\(x = ?, \quad \\)

enter the smallest solution

Explanation:

Set up the equation and cross-multiply

$$
LATEXBLOCK0
$$

Expand and rearrange into standard quadratic form

$$
LATEXBLOCK1
$$

Factor the quadratic equation and solve for x

$$
LATEXBLOCK2
$$

Both values are valid as they do not make any denominator zero (\(x
eq 6\) and \(x
eq 0\)). The smallest solution is \(-4\).

Answer:

Solve the following rational equation.

$$\frac{5}{x - 6} = \frac{x + 6}{x}$$

\(x =\) <blank>\(-4\)</blank>, <blank>\(9\)</blank>

Enter the smallest solution first.