Originally Posted by
Sean12345 1) $\displaystyle \frac {3}{49z^3y}-\frac{1}{21z^2y}$
$\displaystyle \implies \frac {3(21z^2y)-49z^3y}{(21z^2y)(49z^3y)}$
$\displaystyle \implies \frac {63z^2y-49z^3y}{1029z^5y^2}$
$\displaystyle \implies \frac {9z^2y-7z^3y}{147z^5y^2}$
$\displaystyle \implies \frac {z^2(9y-7zy)}{147z^5y^2}$
$\displaystyle \implies \frac {y(9-7z)}{147z^3y^2}$
$\displaystyle \implies \frac {9-7z}{147z^3y}$
2) Correct.
3) Correct.
4) Correct.
5)$\displaystyle \frac{\frac{1}{x}+\frac{1}{y}}{\frac{x^2-y^2}{xy}}$
$\displaystyle \implies\frac{\frac{x+y}{xy}}{\frac{x^2-y^2}{xy}}$
$\displaystyle \implies\frac{x+y}{xy}\cdot\frac{xy}{x^2-y^2}$
$\displaystyle \implies\frac{x+y}{x^2-y^2}$
$\displaystyle
\implies\frac{1}{x-y}
$
It's late so i might have made a mistake, please check.