Question

question 20 - 1 point

rewrite as equivalent rational expressions with denominator \\((a - 7)(a - 2)(a + 8)\\):

\\\frac{3}{a^2 - 9a + 14}, \frac{8a}{a^2 + a - 56}\\

provide your answer below:

\\(\frac{\box}{(a - 7)(a - 2)(a + 8)}\\) and \\(\frac{\box}{(a - 7)(a - 2)(a + 8)}\\)

Explanation:

Factor the denominators

Using the Factoring Trinomials knowledge point

$$
LATEXBLOCK0
$$

Identify the missing factors

Using the Equivalent Rational Expressions knowledge point

$$
LATEXBLOCK1
$$

Rewrite the first expression

Using the Equivalent Rational Expressions knowledge point

$$ \frac{3}{a^2 - 9a + 14} = \frac{3(a + 8)}{(a - 7)(a - 2)(a + 8)} $$

Rewrite the second expression

Using the Equivalent Rational Expressions knowledge point

$$ \frac{8a}{a^2 + a - 56} = \frac{8a(a - 2)}{(a - 7)(a - 2)(a + 8)} $$

Answer:

Rewrite as equivalent rational expressions with denominator \((a-7)(a-2)(a+8)\):

$$\frac{3}{a^2-9a+14}, \frac{8a}{a^2+a-56}$$

Provide your answer below:
<blank>\(\frac{3(a + 8)}{(a - 7)(a - 2)(a + 8)}\)</blank> and <blank>\(\frac{8a(a - 2)}{(a - 7)(a - 2)(a + 8)}\)</blank>