Question

Rearrange y + 3 = x(y + 2) to make y the subject of the formula.

Answer 1

To rearrange the equation \( y + 3 = x(y + 2) \) and make \( y \) the subject, follow these steps:

1. Expand the right side:
\[
y + 3 = xy + 2x
\]

2. Move all terms involving \( y \) to one side and constant terms to the other side:
\[
y - xy = 2x - 3
\]

3. Factor out \( y \) on the left:
\[
y(1 - x) = 2x - 3
\]

4. Now, divide both sides by \( (1 - x) \) to solve for \( y \):
\[
y = \frac{2x - 3}{1 - x}
\]

Thus, \( y \) is isolated as:
\[
y = \frac{2x - 3}{1 - x}
\]