Question

solve each rational equation. remember to check for any extraneous so

1. \\(\frac{1}{x^2} = \frac{1}{3x^2} + \frac{1}{3x}\\) \\(\text{lcd: }\underline{}\\) 2) \\(\frac{1}{x - 4} = \frac{5x - }{x^2}\\)

Explanation:

Step1: Identify denominators

The denominators in the equation $\frac{1}{x^2} = \frac{1}{3x^2} + \frac{1}{3x}$ are $x^2$, $3x^2$, and $3x$.

Step2: Find LCD

To find the least common denominator (LCD), we consider the highest power of each factor. For the variable $x$, the highest power is $x^2$. For the constant factor, the highest common multiple of 1 and 3 is 3. So, the LCD is the product of these, which is $3x^2$.

Answer:

$3x^2$