Question

Find the last common denominator for these two rational expressions

Answer 1

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

Explanation:

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

`(x^3)/(x^2-2x+1)` and
`(-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).