Question

solve the following rational equation.

\\\frac{3}{x + 2} = \frac{x + 9}{x + 1}\\

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

enter the smallest solution first.

Explanation:

Identify excluded values

Using the Rational Equations knowledge point

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

Cross-multiply to clear fractions

Using the Solving Rational Equations knowledge point

$$
LATEXBLOCK0
$$

Rearrange into standard quadratic form

Using the Solving Rational Equations knowledge point

$$
LATEXBLOCK1
$$

Factor the quadratic equation

Using the Factoring Trinomials knowledge point

$$ (x + 3)(x + 5) = 0 $$

Solve for x and check solutions

Using the Solving Rational Equations knowledge point

$$
LATEXBLOCK2
$$

Answer:

Solve the following rational equation.

$$\frac{3}{x + 2} = \frac{x + 9}{x + 1}$$

\(x =\) <blank>-5</blank>, <blank>-3</blank>
Enter the smallest solution first.