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JAMB 1987 · UME · Q27

Simplify x2−y22x2+xy−y2\dfrac{x^2 - y^2}{2x^2 + xy - y^2}.

Worked solution (try it first)
  1. The top is a difference of two squares: x2−y2=(x−y)(x+y)x^2 - y^2 = (x - y)(x + y).
  2. Factorise the bottom: 2x2+xy−y2=2x2+2xy−xy−y22x^2 + xy - y^2 = 2x^2 + 2xy - xy - y^2, which is (2x−y)(x+y)(2x - y)(x + y).
  3. Cancel the common factor x+yx + y.
  4. This leaves x−y2x−y\dfrac{x - y}{2x - y}, option C.

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