Question
The following equation is being multiplied by the LCD: Complete the multiplication to eliminate the denominators. \( \frac{x+2}{3 x}-\frac{1}{x-2}=\frac{x-3}{3 x} \) \( (3 x)(x-2)\left[\frac{x+2}{3 x}-\frac{1}{x-2}\right]=(3 x)(x-2)\left[\frac{x-3}{3 x}\right] \) The resulting equation is
Ask by Gross Gray. in the United States
Mar 11,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
After multiplying both sides by the LCD \(3x(x-2)\), the equation becomes:
\[
(x+2)(x-2) - 3x = (x-3)(x-2)
\]
Solution
\[
(3x)(x-2)\left[\frac{x+2}{3x}\right] = (x+2)(x-2)
\]
\[
(3x)(x-2)\left[\frac{1}{x-2}\right] = 3x
\]
\[
(3x)(x-2)\left[\frac{x-3}{3x}\right] = (x-3)(x-2)
\]
Thus, multiplying the entire equation
\[
\frac{x+2}{3x} - \frac{1}{x-2} = \frac{x-3}{3x}
\]
by the LCD \(3x(x-2)\) yields
\[
(x+2)(x-2) - 3x = (x-3)(x-2).
\]
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution The Deep Dive
When you multiply both sides of the equation by the least common denominator (LCD), which is \(3x(x-2)\), you eliminate the denominators. This would look like: \[ (3x)(x-2) \left[\frac{x+2}{3x} - \frac{1}{x-2}\right] = (3x)(x-2)\left[\frac{x-3}{3x}\right] \] Distributing on the left side gives you: \[ (x - 2)(x + 2) - 3x = (x - 3)(x-2) \] This simplifies further to: \[ x^2 - 4 - 3x = x^2 - 5x + 6 \] Removing \(x^2\) from both sides results in: \[ -4 - 3x = -5x + 6 \] Ultimately, rearranging gives you: \[ 2x - 10 = 0 \quad \text{or} \quad x = 5 \] And there you have your resulting equation!
