Question

perform the subtraction.

\\\frac{6x}{x^2 + 2x - 24} - \frac{x}{x^2 - 36}\\

\\\frac{6x}{x^2 + 2x - 24} - \frac{x}{x^2 - 36} = \text{ } (\text{simplify your answer})\\

Explanation:

Factor the denominators

Using the Rational Expressions knowledge point

$$
LATEXBLOCK0
$$

Find the least common denominator

Using the Rational Expressions knowledge point

$$ \text{LCD} = (x + 6)(x - 4)(x - 6) $$

Rewrite fractions with the LCD

Using the Rational Expressions knowledge point

$$
LATEXBLOCK1
$$

Subtract and simplify the numerator

Using the Rational Expressions knowledge point

$$
LATEXBLOCK2
$$

Write the final simplified expression

Using the Rational Expressions knowledge point

$$ \frac{5x^2 - 32x}{(x+6)(x-4)(x-6)} $$

Answer:

Perform the subtraction.

\(\frac{6x}{x^2+2x-24} - \frac{x}{x^2-36} =\) <blank>\(\frac{5x^2-32x}{(x+6)(x-4)(x-6)}\)</blank> (Simplify your answer)