Find the distance between the points A(−3, 2) and B(4, −6). Find the acute angle between the lines 2x + 3y = 5 and 3x + 2y = 1 correct to one decimal place.

Dividing by a fraction is equivalent to multiplying by its reciprocal.

$$\frac{x-y}{y+x} \div \frac{y-x}{x+y} = \frac{x-y}{y+x} \times \frac{x+y}{y-x}$$

Notice that $y+x$ is the same as $x+y$.
Also, $y-x$ is the negative of $x-y$, i.e., $y-x = -(x-y)$.

Substitute these into the expression:

$$\frac{x-y}{x+y} \times \frac{x+y}{-(x-y)}$$

The $(x+y)$ in the denominator of the first fraction cancels with the $(x+y)$ in the numerator of the second fraction.
The $(x-y)$ in the numerator of the first fraction cancels with the $(x-y)$ in the denominator of the second fraction.

$$\frac{\cancel{(x-y)}}{\cancel{(x+y)}} \times \frac{\cancel{(x+y)}}{-\cancel{(x-y)}}$$

This leaves:

$$1 \times \frac{1}{-1}$$

$$1 \times (-1) = -1$$

The simplified expression is:

$$-1$$