Question

question

add: \\(\frac{9}{4u^2 - 19u + 21} + \frac{4u}{4u^2 + 5u - 21}\\).

provide your answer below:

Explanation:

Factor the denominators

Using the Trinomial Factorization knowledge point

$$
LATEXBLOCK0
$$

Find the least common denominator

Using the Least Common Denominator knowledge point

$$ \text{LCD} = (4u - 7)(u - 3)(u + 3) $$

Rewrite each expression with the LCD

Using the Equivalent Rational Expressions knowledge point

$$
LATEXBLOCK1
$$

Combine and simplify the numerators

Using the Adding Rational Expressions knowledge point

$$
LATEXBLOCK2
$$

Write the final rational expression

$$ \frac{4u^2 - 3u + 27}{(4u - 7)(u - 3)(u + 3)} $$

Answer:

Add: \(\frac{9}{4u^2 - 19u + 21} + \frac{4u}{4u^2 + 5u - 21}\).

Provide your answer below:
<blank>\(\frac{4u^2-3u+27}{(4u-7)(u-3)(u+3)}\)</blank>