Question

lesson 25 review - solving rational equations
3
\\(\frac{x}{x - 2} - \frac{2}{x + 4} = \frac{12}{x^2 + 2x - 8}\\)
lcd = (x + 4)(x - 2)
1 factor denominators
2 find lcd
3 multiply to create lcd
4 solve using numerator
5 check for extraneous solutions!
\\(\frac{x}{(x - 2)} - \frac{2}{(x + 4)} = \frac{12}{(x + 4)(x - 2)}\\)
\\(\frac{x}{(x - 2)}(x + 4) - \frac{2}{(x + 4)}(x - 2) = \frac{12}{(x + 4)(x - 2)}\\)
\\(x(x + 4) - 2(x - 2) = 12\\)
\\(x^2 + 4x - 2x + 4 = 12\\)
\\(x^2 + 2x - 8 = 0\\)
\\((x + 4)(x - 2) = 0\\)
\\(x + 4 = 0\\) \\(x - 2 = 0\\)
multiple - choice question
from where she left off, make sure you have it copied.
then complete the solving.
which two x - values come out of the tiny equations she just finished writing?
4 and -2
-4 and 2
rewatch

Explanation:

Step1: Analyze the last equation

We have \((x + 4)(x - 2)=0\). By the zero - product property, if \(ab = 0\), then either \(a = 0\) or \(b = 0\).

Step2: Solve for x

For the factor \(x + 4\), set \(x+4 = 0\), we get \(x=-4\). For the factor \(x - 2\), set \(x - 2=0\), we get \(x = 2\).

Answer:

-4 and 2 (the option with text "-4 and 2")