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**Hint:**For getting the value of a variable in this kind of fraction form, you just need to simplify the fraction, if simplification is possible with the fraction term then first simplify it and then cross multiply and find the solution of the variable, if simplification is not possible then just simply put every term in one side of equation and the variable on the other side to get the solution.

**Complete step by step solution:**

The given question is to simplify the fraction equation

\[\dfrac{{hi}}{{ho}} = - \dfrac{{di}}{{do}}\]

And to find the value of “do”

Assuming that the given terms in the fraction part are solely independent, that is the given variables can’t be reduced by cancelling the similar letters in denominator and numerator we get:

\[

\Rightarrow \dfrac{{hi}}{{ho}} = - \dfrac{{di}}{{do}} \\

\Rightarrow do \times \dfrac{{hi}}{{ho}} = - di \\

\Rightarrow do = - di \times \dfrac{{ho}}{{hi}} \\

\]

This is our final solution for the variable asked in the question.

**Additional Information:**Here you can also assume the terms as some other variable to get no confusion with the cross multiplication and getting the solution of the equation, but since there are only two –two variables written in the terms of fraction so you can solve directly also.

**Note:**To get solution of such question you need to clear with the cross multiplication rule, that is when you multiply the denominator of the left hand side equation term to the right hand side then it will multiply in the numerator part of the right hand side equation term and vice versa for the case of denominator.

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