Question

solve the following rational equation.

\\(\frac{x + 6}{x + 1} = \frac{4}{x - 2}\\)

\\(x = ?, \square\\)

enter the smallest solution first

Explanation:

State the excluded values

Using the Rational Equations knowledge point

$$ x e -1, \quad x e 2 $$

Cross-multiply to eliminate fractions

Using the Solving Rational Equations knowledge point

$$ (x + 6)(x - 2) = 4(x + 1) $$

Expand and simplify the equation

Using the Solving Rational Equations knowledge point

$$
LATEXBLOCK0
$$

Solve for x

Using the Factoring Trinomials knowledge point

$$
LATEXBLOCK1
$$

Identify the smallest solution

Using the Solving Rational Equations knowledge point

$$
LATEXBLOCK2
$$

Answer:

Solve the following rational equation.

$$\frac{x + 6}{x + 1} = \frac{4}{x - 2}$$

\(x =\) <blank>-4</blank>, <blank>4</blank>
Enter the smallest solution first.