5 Linear and nonlinear equations; Question 5.30

[Eigenvalue]

5.30. Solve [tex]\frac{1}{p}[/tex]+[tex]\frac{1}{q}[/tex]=[tex]\frac{1}{f}[/tex] for q

[Eigenvalue]

[tex]\frac{1}{p}[/tex]+[tex]\frac{1}{q}[/tex]=[tex]\frac{1}{f}[/tex]

Multiply both sides by pqf: qf+pf=pq
pf=pq-qf
pf=q(p-f)
q=[tex]\frac{pf}{p-f}[/tex]

pq+qf=pq
f(p+q)=pq
f=[tex]\frac{pq}{p+q}[/tex]

pf-pq=-qf
p(f-q)=-qf
p=[tex]\frac{-qf}{f-q}[/tex]