Question

F₁ + F₂ = Fr and F₁ . d₁= F₂.d₂ Solve for F₁ in terms of Fr, d₁, and d₂

Answer 1

F₁ =
`(F_(r)d_(2) )/(d_(2)+d_(1) )`

Explanation:

given

F₁ + F₂ =
`F_(r)` → (1)

and

F₁d₁ = F₂d₂

express F₂ in terms of F₁d₁ by dividing both sides by d₂

`(F_(1)d_(1) )/(d_(2) )` = F₂ ← substitute into (1)

F₁ +
`(F_(1)d_(1) )/(d_(2) )` =
`F_(r)`

multiply through by d₂ to clear the fraction ( d₂ ≠ 0 )

F₁d₂ + F₁d₁ =
`F_(r)` d₂ ← factor out
`F_(1)` from each term on the left side

F₁(d₂ + d₁) =
`F_(r)` d₂ ← divide both sides by (d₂ + d₁)

F₁ =
`(F_(r)d_(2) )/(d_(2)+d_(1) )`