Question

solve the equation.

\\\frac{4b}{b+2} - \frac{6}{b+4} = \frac{3b^2 + 14b}{b^2 + 6b + 8}\\

the solution set is

Explanation:

Factor the denominators

Using the Factoring Polynomials knowledge point

$$ b^2 + 6b + 8 = (b+2)(b+4) $$

Find the common denominator

Using the Fractional Equations knowledge point

$$
LATEXBLOCK0
$$

Clear the fractions

Using the Fractional Equations knowledge point

$$
LATEXBLOCK1
$$

Solve the quadratic equation

Using the Fractional Equations knowledge point

$$
LATEXBLOCK2
$$

Check for extraneous solutions

Since \(b
e -2\), the only valid solution is \(b = 6\).

Answer:

Solve the equation.

$$\frac{4b}{b+2} - \frac{6}{b+4} = \frac{3b^2+14b}{b^2+6b+8}$$

The solution set is <blank>\(\{6\}\)</blank>.