Question

current objective
add and subtract rational expressions whose

question
simplify: \frac{-d^2 - 6d + 4}{d^2 - 1} - \frac{-2d^2 - 6d + 5}{-d^2 + 1}.

provide your answer below:

Explanation:

Identify opposite denominators

Using the Opposite Factors knowledge point

$$ -d^2 + 1 = -(d^2 - 1) $$

Rewrite the subtraction as addition

Using the Adding Rational Expressions and Opposite Factors knowledge points

$$
LATEXBLOCK0
$$

Combine the numerators over the common denominator

Using the Adding Rational Expressions knowledge point

$$
LATEXBLOCK1
$$

Factor the numerator and denominator to check for simplification

Using the Greatest Common Factor Factoring and Difference of Squares knowledge points

$$
LATEXBLOCK2
$$

Since the trinomial \(d^2 + 4d - 3\) cannot be factored further over the integers to produce factors of \((d - 1)\) or \((d + 1)\), the expression is fully simplified.

Answer:

\(\frac{-3d^2 - 12d + 9}{d^2 - 1}\)