### 9.1.8 Multiplication by the conjugate quantity

The mult_conjugate tries to remove square roots from the bottom of an expression.

- mult_conjugate takes expr, an expression. The denominator or numerator is supposed to contain a square root.
- mult_conjugate(expr) returns the following:
  - If expr is a fraction and the denominator contains a square root, then this expression is returned with the numerator and denominator multiplied by the conjugate of the denominator.
  - If expr is a fraction and the numerator, but not the denominator, contains a square root (if expr is not a fraction, it is regarded as a fraction with a denominator of 1), then this expression is returned with the numerator and denominator multiplied by the conjugate of the numerator.

#### Examples

mult_conjugate((2+sqrt(2))/(2+sqrt(3)))

⎛ ⎜ ⎝ | 2+ | √ |
2
| ⎞ ⎟ ⎠ | ⎛ ⎜ ⎝ | 2− | √ |
3
| ⎞ ⎟ ⎠
⎛ ⎜ ⎝ | 2+ | √ |
3
| ⎞ ⎟ ⎠ | ⎛ ⎜ ⎝ | 2− | √ |
3
| ⎞ ⎟ ⎠

mult_conjugate((2+sqrt(2))/(sqrt(2)+sqrt(3)))

⎛ ⎜ ⎝ | 2+ | √ |
2
| ⎞ ⎟ ⎠ | ⎛ ⎜ ⎝ | − | √ |
2
| + | √ |
3
| ⎞ ⎟ ⎠
⎛ ⎜ ⎝ | √ |
2
| + | √ |
3
| ⎞ ⎟ ⎠ | ⎛ ⎜ ⎝ | − | √ |
2
| + | √ |
3
| ⎞ ⎟ ⎠

mult_conjugate((2+sqrt(2))/2)

⎛ ⎜ ⎝ | 2+ | √ |
2
| ⎞ ⎟ ⎠ | ⎛ ⎜ ⎝ | 2− | √ |
2
| ⎞ ⎟ ⎠
2 | ⎛ ⎜ ⎝ | 2− | √ |
2
| ⎞ ⎟ ⎠