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GNU Emacs Calc 2.02 Manual

3.7.52 Rewrites Tutorial Exercise 1

We'll use Big mode to make the formulas more readable.

___ 2 + V 2 1: (2 + sqrt(2)) / (1 + sqrt(2)) 1: -------- . ___ 1 + V 2 . ' (2+sqrt(2)) / (1+sqrt(2)) RET d B

Multiplying by the conjugate helps because (a+b) (a-b) = a^2 - b^2.

___ ___ 1: (2 + V 2 ) (V 2 - 1) . a r a/(b+c) := a*(b-c) / (b^2-c^2) RET

___ ___ 1: 2 + V 2 - 2 1: V 2 . . a r a*(b+c) := a*b + a*c a s

(We could have used a x instead of a rewrite rule for the second step.)

The multiply-by-conjugate rule turns out to be useful in many different circumstances, such as when the denominator involves sines and cosines or the imaginary constant i.