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### 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`.

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