When to omit pronoun after "but"?

Question

I have the two sentences:

Original sentences:

"I baked an apple pie, but I forgot to put cinnamon in it."

"Sonia speaks English but does not write it."

My questions:

1. Can I write: I baked an apple pie, but forgot to put cinnamon in it. (I removed "I" after "but")? Is it correct?

2. Is is it correct to write: "Sonia speaks English but she does not write it."?

3. What is the rule to omit pronoun after "but"? Please explain this using the original sentences.

Related: Is it always necessary to repeat the pronoun before each verb?

Answer 1

I baked an apple pie, but forgot to put cinnamon in it.
I baked an apple pie, but I forgot to put cinnamon in it.

Sonia speaks English but does not write it.
Sonia speaks English but she does not write it.

Both forms of your two sentences are equivalent in meaning. The additional pronoun can be left out if there is no ambiguity in the understanding

Susan and I baked an apple pie, but forgot to put cinnamon in it.

is understood as

Susan and I baked an apple pie, but we forgot to put cinnamon in it.

and is different than

Susan and I baked an apple pie, but she forgot to put cinnamon in it.
Susan and I baked an apple pie, but I forgot to put cinnamon in it.

Since your examples only have a single subject being referred to, there is no ambiguity.