Question

Find the last common denominator for these two rational expressions

Answer 1

Answer:

Least common denominator = (x - 1)²(x - 2)

Step-by-step explanation:

Least common denominator of two rational expressions = LCM of the denominator of the expressions.

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

Factorize the denominators of these rational expressions,

Since, $x^{2}-2x+1$ = x² - 2x + 1

                             = (x - 1)²

And x² - 3x + 2 = x² - 2x - x + 2

                         = x(x - 2) -1(x - 2)

                         = (x - 1)(x - 2)

Now LCM of the denominators = (x - 1)²(x - 2)

Therefore, Least common denominator will be (x - 1)²(x - 2).