Question

lesson 2.5 review - solving rational equations
3
\\(\frac{x}{x - 2} - \frac{2}{x + 4} = \frac{12}{x^2 + 2x - 8}\\)
① factor denominators
② find lcd
③ multiply to create lcd
④ solve using numerator
⑤ check for extraneous solutions
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multiple - choice question
use guess and check method. which of the following is the factored form of \\(x^2 + 2x - 8\\)
\\((x - 8)(x + 1)\\)
\\((x - 4)(x + 2)\\)
\\((x + 4)(x - 2)\\)
\\((x - 2)(x - 4)\\)
rewatch

Explanation:

Step1: Recall factoring quadratic

To factor \(x^2 + 2x - 8\), we need two numbers that multiply to \(-8\) and add to \(2\).

Step2: Find the numbers

The numbers are \(4\) and \(-2\) because \(4\times(-2)= -8\) and \(4 + (-2)=2\).

Step3: Write the factored form

So, \(x^2 + 2x - 8=(x + 4)(x - 2)\).

Answer:

\((x + 4)(x - 2)\) (corresponding to the option with this factored form, i.e., the third option in the multiple - choice list: \((x + 4)(x - 2)\))