MCQ
The factorisation of $(\frac{{\text{x}^2}}{{\text{y}}^2}-2+\frac{{\text{y}^2}}{{\text{x}^2}})\text{x}\not=0$ is:
  • A
    $(\frac{\text{x}}{\text{y}}+\frac{\text{y}}{\text{x}})^2$
  • $(\frac{\text{x}}{\text{y}}-\frac{\text{y}}{\text{x}})^2$
  • C
    $(\frac{\text{x}}{\text{y}}-1)^2$
  • D
    $(\frac{\text{x}}{\text{y}}+1)^2$

Answer

Correct option: B.
$(\frac{\text{x}}{\text{y}}-\frac{\text{y}}{\text{x}})^2$
$=\frac{​​\text{x}^2}{\text{y}^2}-2+\frac{\text{y}^2}{\text{x}^2}$
$=(\frac{\text{x}}{\text{y}})^2-2(\frac{\text{x}}{\text{y}})(\frac{\text{y}}{\text{x}})+(\frac{\text{y}}{\text{x}})^2$
$=(\frac{\text{x}}{\text{y}}-\frac{\text{y}}{\text{x}})^2$

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