What is the standard quadratic form of (x + 2)/(x − 1) + (x − 1)/(x + 2) = 5/2?
Answer and explanation
Correct answer: x² + x − 20 = 0
First note the restrictions x ≠ 1 and x ≠ −2, because the original denominators cannot be zero. Multiplying the equation by 2(x − 1)(x + 2) gives 2(x + 2)² + 2(x − 1)² = 5(x − 1)(x + 2). Expanding, the left side is 4x² + 4x + 10, while the right side is 5x² + 5x − 10. Moving all terms to one side yields x² + x − 20 = 0. Therefore option A is correct. The other choices contain an incorrect sign, constant term, or leading coefficient.
Frequently asked questions
What is the correct answer to this question?
x² + x − 20 = 0
Why is this the correct answer?
First note the restrictions x ≠ 1 and x ≠ −2, because the original denominators cannot be zero. Multiplying the equation by 2(x − 1)(x + 2) gives 2(x + 2)² + 2(x − 1)² = 5(x − 1)(x + 2). Expanding, the left side is 4x² + 4x + 10, while the right side is 5x² + 5x − 10. Moving all terms to one side yields x² + x − 20 = 0. Therefore option A is correct. The other choices contain an incorrect sign, constant term, or leading coefficient.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Introduction to Quadratic Equations.
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