Next: Rewrites Tutorial Exercise 2, Previous: Algebra Tutorial Exercise 4, Up: Answers to Exercises [Contents][Index]

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

```
___
V 2 + 2
1: (2 + sqrt(2)) / (1 + sqrt(2)) 1: ---------
. ___
V 2 + 1
.
' (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: V 2 . a r a*(b+c) := a*b + a*c

(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`

.