Incorrect substitution into fraction

Questions
,
1

I input

(x + y)/(z + w), x = A*y, z=B*w

to WolframAlpha, yielding

enter image description here

yet by substitution, we find

\frac{x + y}{z + w} = \frac{Ay + y}{Bw + w}

Is there a way to query that forces correct output? This is a minimal reproduction of a more complicated original where I can’t just plug in.

2

I don’t use WolframAlpha much, so I’m inferring a lot here. The {} you see in WA’s interpretation of your input makes me think it naturally assumes comma separated expressions should be interpreted as a list. And the fact that only one substitution was applied in the next block makes me think that WA assumes that substitutions are defined by the last expression given.

I was able to get it to do what I think you want with this input

(x + y)/(z + w) where x = A*y and z = B*w
3

Uh oh… I trusted several outputs with my input format, where I couldn’t tell it was mistaken. I think this is a seriously misleading and should be addressed.

Replacing the fraction with x / y yields 0, which makes no sense, yet w / z works as expected. In the original fraction, WA arbitrarily setting x=0 instead of just leaving it as x + y also makes no sense.

You appear to be correct, thanks! where x = A*y, z = B*w also works.

(Let me know if I can “accept” a post like on Github or Stack Exchange, as the resolution)