Answer:
see explanation
Step-by-step explanation:
Multiply through by the lowest common multiple of u, v and f, that is uvf
uvf × [tex]\frac{1}{v}[/tex] + uvf × [tex]\frac{1}{u}[/tex] = uvf × [tex]\frac{1}{f}[/tex], that is
uf + vf = uv ← factor out f on the left side → (1)
f(u + v) = uv ← divide both sides by (u + v)
f = [tex]\frac{uv}{u+v}[/tex]
(b)
Using line (1)
uf + vf = uv ( subtract uv from both sides )
uf + vf - uv = 0 ( subtract uf from both sides )
vf - uv = - uf ← factor out v on the left side
v(f - u) = - uf ← divide both sides by (f - u)
v = - [tex]\frac{uf}{f-u}[/tex]
