Question

How do you solve for do in `(hi)/(ho)=-(di)/(do)`?

Answer 1

`(do) = -(ho xx di)/(hi)`

Explanation:

If an equation has one fraction on each side, you can get rid of the denominators by cross-multiplying.

`(hi)/(ho) = -(di)/(color(red)(do))`

`hixxcolor(red)(do) = -ho xx di " "larr div "(hi)`

`color(red)(do) = -(ho xx di)/(hi)`

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If an equation has one fraction on each side, you can invert the whole equation. This will put `do` in the numerator.

`(ho)/(hi) = - (color(red)(do))/(di)" "larr xx -di`

`-(ho xx di)/(hi) =color(red)(do)`

`color(red)(do) = -(ho xx di)/(hi)`