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।
If (f(x)=\frac{2x}{x-2-4}) and (g(x)=\frac{1}{x-2}), choose the correct simplified form of ((f-g)(x)).
Explanation opens after your attempt
Correct Answer
A. \(\frac{1}{x+2},\ x\ne\pm2\)
Concept
(\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.
Why this answer is correct
The correct answer is A. \(\frac{1}{x+2},\ x\ne\pm2\). (\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.
Exam Tip
(\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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