Question

subtract the rational expressions to find the difference: \\(\frac{x^2 - 2}{4x - 7} - \frac{x + 4}{4x - 7}\\) (1 point) \\(\frac{-6}{4x - 7}\\) \\(\frac{x^2 - x - 6}{4x - 7}\\) \\(\frac{x^2 - x + 2}{4x - 7}\\) \\(\frac{x^2 - x - 6}{8x - 14}\\)

Explanation:

Step1: Subtract numerators (common denominator)

Since the denominators are the same ($4x - 7$), we subtract the numerators: $(x^2 - 2) - (x + 4)$.
$$(x^2 - 2) - (x + 4) = x^2 - 2 - x - 4$$

Step2: Simplify the numerator

Combine like terms: $x^2 - x + (-2 - 4) = x^2 - x - 6$.

Step3: Write the result over the common denominator

The denominator remains $4x - 7$, so the expression becomes $\frac{x^2 - x - 6}{4x - 7}$.

Answer:

$\frac{x^2 - x - 6}{4x - 7}$ (corresponding to the option with this expression)