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If (f(x)=\frac{2x}{x^2-4}) and (g(x)=\frac{1}{x-2}), choose the correct simplified form of ((f-g)(x)).यदि (f(x)=\frac{2x}{x^2-4}) और (g(x)=\frac{1}{x-2}) हैं, तो ((f-g)(x)) का सही सरल रूप चुनिए।
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (\frac{1}{x+2},\ x\ne\pm2)(\frac{1}{x+2},\ x\ne\pm2)
(\frac{2x}{(x-2)(x+2)}-\frac{x+2}{(x-2)(x+2)}=\frac{x-2}{(x-2)(x+2)}). Hence the simplified form is (\frac{1}{x+2}), but (x=\pm2) remain excluded.(\frac{2x}{(x-2)(x+2)}-\frac{x+2}{(x-2)(x+2)}=\frac{x-2}{(x-2)(x+2)})। इसलिए सरल रूप (\frac{1}{x+2}) है, पर (x=\pm2) हटे रहेंगे।
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