Question

please solve this answer in proper method​

Answer 1

Answer:

Step-by-step explanation:

$x = \frac{6pq}{p+q}$  and  $x = \frac{6pq}{p+q}$

∴ $x = \frac{3p * 2q}{p + q}$     ∴$x = \frac{2p * 3q}{p + q}$

∴ $\frac{x}{3p} = \frac{2q}{p +q}$      ∴ $\frac{x}{3q} = \frac{2p}{p +q}$

By componendo- dividendo

$\frac{x+3p}{x - 3p} = \frac{2q + p + q}{2q - (p +q)}$   and  $\frac{x+3q}{x - 3q} = \frac{2p + p + q}{2p - (p +q)}$

∴  $\frac{x+3p}{x - 3p} = \frac{ p + 3q}{q -p}$     and    $\frac{x+3q}{x - 3q} = \frac{3p+ q}{p -q}$

∴  $\frac{x+3p}{x - 3p} + \frac{ x + 3q}{x - 3q}$       =       $\frac{p+3q}{q -p } - \frac{3p+ q}{p -q}$

= $\frac{p + 3q}{q - p} - \frac{3p + q}{q - p} = \frac{p + 3q - 3p - q}{q - p}$

∴ $\frac{x+3p}{x - 3p} + \frac{x+3q}{x - 3q} = \frac{2q -2p}{q -p} = 2$

Hope this helps you dear!!!