TITLE: Visual proof for $\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}$
QUESTION [5 upvotes]: I've found visualizations of simple mathematical concepts to be a really useful tool in building intuition for more complex mathematical concepts. For example, this visualization of $(a + b)(c + d) = ac + ad + bc + bd$ can be used to visualize the calculus product rule.
That being said, does anyone know of a visual way to show the following equation?
$$
\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}
$$

REPLY [2 votes]: Here is my version which depends on similar triangles.