(k^2-7k+10)/(k-1)

less than a minute read Jun 16, 2024

Simplifying the Expression (k^2 - 7k + 10)/(k-1)

This expression represents a rational function, where the numerator and denominator are both polynomials. Simplifying it involves factoring and potentially canceling out common factors.

Factoring the Numerator

First, we factor the quadratic expression in the numerator:

(k^2 - 7k + 10) = (k - 5)(k - 2)

Rewriting the Expression

Now, we can rewrite the entire expression:

(k^2 - 7k + 10)/(k - 1) = (k - 5)(k - 2)/(k - 1)

Restrictions

It's important to note that the expression is undefined when the denominator is zero. Therefore, k cannot be equal to 1.

Final Simplification

Since there are no common factors between the numerator and denominator, the expression is already simplified.

Therefore, the simplified form of (k^2 - 7k + 10)/(k-1) is (k - 5)(k - 2)/(k - 1), where k ≠ 1.