Question:
Tick (✓) the correct answer:
$\left(\frac{1}{x}+\frac{1}{y}\right)\left(\frac{1}{x}-\frac{1}{y}\right)=?$
(a) $\left(\frac{1}{x^{2}}-\frac{1}{y^{2}}\right)$
(b) $\left(\frac{1}{x^{2}}+\frac{1}{y^{2}}\right)$
(c) $\left(\frac{1}{x^{2}}+\frac{1}{y^{2}}-\frac{1}{x y}\right)$
(d) $\left(\frac{1}{x^{2}}-\frac{1}{y^{2}}+\frac{1}{x y}\right)$
Solution:
(a) $\left(\frac{1}{x^{2}}-\frac{1}{y^{2}}\right)$
$\left(\frac{1}{x}+\frac{1}{y}\right)\left(\frac{1}{x}-\frac{1}{y}\right)$
$\Rightarrow$ According to the formula $(a+b)(a-b)=(a)^{2}-(b)^{2}:$
$\Rightarrow\left(\frac{1}{x^{2}}-\frac{1}{y^{2}}\right)$