Math Problem Statement

x 2

7 x + 12 x

4 dengan x 2

x

2 x + 1 dengan x≠4 dan x≠-1 adalah

Solution

To simplify the expression:

x27x+12x2x2x+1\frac{x^2 - 7x + 12}{x^2 - x - 2x + 1}

given that x4x \neq 4 and x1x \neq -1, we will follow these steps:

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

    • Numerator: x27x+12x^2 - 7x + 12

      • Find two numbers that multiply to 12 and add up to -7, which are -3 and -4.
      • Thus, x27x+12=(x3)(x4)x^2 - 7x + 12 = (x - 3)(x - 4).
    • Denominator: x2x2x+1x^2 - x - 2x + 1

      • Group terms: x23x+1x^2 - 3x + 1
      • Further simplify

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Math Problem Analysis

Mathematical Concepts

Algebra
Polynomial Factorization
Simplification of Rational Expressions

Formulas

Factoring quadratics: x^2 + bx + c = (x - p)(x - q) where p and q are roots
Simplifying rational expressions: (A/B) = (factorized numerator) / (factorized denominator)

Theorems

Factorization of quadratics
Simplification of rational expressions

Suitable Grade Level

Grades 8-10