Question

evaluate \frac{cd - 6c + 2}{-5c - 9d^3 + 9d + 10} when c = 2 and d = -2. enter an integer or a fraction in simplest form.

Explanation:

Identify the expression and given values

We are given the rational expression:

$$ \frac{cd - 6c + 2}{-5c - 9d^3 + 9d + 10} $$

We need to evaluate this expression when \(c = 2\) and \(d = -2\).

Evaluate the numerator

Using the Evaluating Rational Expressions knowledge point, we substitute \(c = 2\) and \(d = -2\) into the numerator:

$$
LATEXBLOCK0
$$

Evaluate the denominator

Next, we substitute \(c = 2\) and \(d = -2\) into the denominator:

$$
LATEXBLOCK1
$$

Simplify the resulting fraction

Using the Fraction Arithmetic knowledge point, we write the evaluated expression as a fraction and simplify it to its simplest form:

$$ \frac{\text{Numerator}}{\text{Denominator}} = \frac{-14}{54} = \frac{-7 \times 2}{27 \times 2} = -\frac{7}{27} $$

Answer:

\(-\frac{7}{27}\)