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If \(f(x)=x+2\) and \(g(x)=x^2-4\), what are the correct simplified form and domain of \(\left(\frac{g}{f}\right)(x)\)?यदि \(f(x)=x+2\) और \(g(x)=x^2-4\) हैं, तो \(\left(\frac{g}{f}\right)(x)\) का सही सरलीकृत रूप और प्रांत क्या होगा?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (x-2,\ x\ne-2)(x-2,\ x\ne-2)
\(\frac{x^2-4}{x+2}=\frac{(x-2)(x+2)}{x+2}=x-2\), but \(x=-2\) remains excluded. Do not forget the original denominator restriction after cancellation.\(\frac{x^2-4}{x+2}=\frac{(x-2)(x+2)}{x+2}=x-2\), पर \(x=-2\) निषिद्ध रहेगा। कटाव के बाद भी मूल हर का प्रतिबंध न भूलें।
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