Question

Solve this problem.​

Answer 1

Answer:

q/pr

Step-by-step explanation:

$\frac{1}{p \alpha + q} + \frac{1}{p \beta + q} = \frac{p \alpha + p \beta + q + q}{(p \alpha + q)(p \beta + q)} \\ \\ = \frac{ p( \alpha + \beta ) + (q + q)}{ {p}^{2} \alpha \beta + pq \alpha + pq \beta + {q}^{2} } \\ \\ = \frac{p( \frac{ - q}{p}) + q + q }{ {p}^{2} ( \frac{r}{p} ) + pq( \frac{ - q}{p} ) + {q}^{2} } \\ \\ \\ = \frac{- q + q+ q}{pr - {q}^{2} + {q}^{2} } \\ \\ \\ = \frac{q}{pr} \\ \\ = \frac{q}{pr}$