Hi StackExchange community,
The formula has this form:
$$ {-7 \pm X \over \sqrt{2} - 3}-3.$$
How can I rewrite this to be more compact ?
Thank you.
2026-03-25 06:08:51.1774418931
Formula Rearrangement
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There are 1 best solutions below
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You could rationalize the denominator of the first term: \begin{align} \frac{-7\pm X}{\sqrt 2-3}-3 &= \frac{-7\pm X}{\sqrt 2-3} \cdot\frac{\sqrt 2+3}{\sqrt 2+3}-3\\[0.4cm] &= \frac{-7(\sqrt{2}+3)\pm(\sqrt 2 +3)X}{\sqrt 2^2-3^2}-3\\[0.4cm] &= \frac{-7(\sqrt 2+3)\pm(\sqrt 2+3)X}{-7}-3\\[0.4cm] &=\sqrt 2 + 3 \mp \frac{\sqrt 2+3}{7}X - 3\\[0.4cm] &= \sqrt 2 \mp \frac{\sqrt 2+3}{7}X. \end{align} Depending on your preferences, you may or may not find this expression to be "more compact".