यदि (f(x)=\frac{2x}{x-2-4}) और (g(x)=\frac{1}{x-2}) हैं, तो ((f-g)(x)) का सरल रूप क्या है?
If (f(x)=\frac{2x}{x-2-4}) and (g(x)=\frac{1}{x-2}), what is the simplified form of ((f-g)(x))?
Explanation opens after your attempt
Correct Answer
A. (\frac{2}{(x-2)(x+2)})
Concept
With common denominator ((x-2)(x+2)), numerator is (2x-(x+2)=x-2), so the form is \(\frac{1}{x+2}\) with \(x\ne\pm2\). Thus option (C) is the simplification.
Why this answer is correct
The correct answer is A. (\frac{2}{(x-2)(x+2)}). With common denominator ((x-2)(x+2)), numerator is (2x-(x+2)=x-2), so the form is \(\frac{1}{x+2}\) with \(x\ne\pm2\). Thus option (C) is the simplification.
Exam Tip
समान हर ((x-2)(x+2)) लेने पर अंश (2x-(x+2)=x-2) होगा, इसलिए \(\frac{1}{x+2}\) पर \(x\ne\pm2\)। सही सरलीकरण विकल्प (C) है।
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