Question

pease help me find the least common denominator for this equation

Answer 1

Explanation

We are required to determine the LCD of the given expression.

$\frac{-3}{x+2}+\frac{5x}{x-1}-\frac{x+2}{x^2-3x+2}$

This is achieved thus:

- First, the demominators of the expression given are:

$\begin{gathered} x+2 \\ x-1 \\ x^2-3x+2 \end{gathered}$

- Next, we factorise the quadratic denominator as follows:

$\begin{gathered} x^2-3x+2 \\ x^2-x-2x+2 \\ (x^2-x)(-2x+2) \\ x(x-1)-2(x-1) \\ (x-1)(x-2) \end{gathered}$

- Finally, the LCD can be calculated as:

Hence, the least common denominator is:

$(x-1)(x-2)(x+2)$

Option C is correct.