(m³ + n² ÷ o²r )^(-1) = (2 + 3r)(√p−q) for real variables m,n,o,p,q and r. Express r as a function of m,n,o,p,q.

Question

With this question do i find what r is to the rest, as in r=..........

And if so, how is the best way to approach this with multiple variables?

I am quite confused with this question.

Answer 1

This is simply an exercise in algebraic manipulation.

The first term simply becomes o²r/(m³ + n²).

Clear fractions, i.e. multiply both sides by (m³ + n²) and expand the right side.

The collect terms. You will have a messy coefficient for r on the left and a messy expression without r on the right.

Then just divide to get r = quotient of two messy terms!