x
2
-
7
x
+
12
x
-
4
 dengan 
x
2
-
x
-
2
x
+
1
 dengan x≠4  dan x≠-1  adalah

To simplify the expression:

\[
\frac{x^2 - 7x + 12}{x^2 - x - 2x + 1}
\]

given that \( x \neq 4 \) and \( x \neq -1 \), we will follow these steps:

1. **Factorize the Numerator and Denominator:**  
   We start by factorizing both the numerator and the denominator.

   - **Numerator**: \( x^2 - 7x + 12 \)
     - Find two numbers that multiply to 12 and add up to -7, which are -3 and -4.
     - Thus, \( x^2 - 7x + 12 = (x - 3)(x - 4) \).

   - **Denominator**: \( x^2 - x - 2x + 1 \)
     - Group terms: \( x^2 - 3x + 1 \)
     - Further simplify

Simplify the expression: (x^2 - 7x + 12) / (x^2 - x - 2x + 1) given that x ≠ 4 and x ≠ -1.

This solution demonstrates the step-by-step process to simplify the rational expression (x^2 - 7x + 12) / (x^2 - x - 2x + 1). Learn key algebraic techniques such as factoring quadratics and simplifying rational expressions. Suitable for Grades 8-10 students.

Math Problem Statement

x 2

7 x + 12 x

4 dengan x 2

x

Solution

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