That's another thing I observed teaching calculus: a lot of students who have problems, are having their difficulties with the algebra they supposedly know, and not so much with the "new" material. In theory, we expect students to already be fluent in this sort of algebraic manipulation; in reality, we recognize that a calculus class provides our students an opportunity to improve at this.
I'm not sure I have any suggestion other than lots of practice. And know that you're not alone, this is a completely natural difficulty.
That's another thing I observed teaching calculus: a lot of students who have problems, are having their difficulties with the algebra they supposedly know
A. You're not alone. In the first video of his Calc I series, Professor Leonard cracks that "Calculus is the class you take to finally fail Algebra".
B. This is hardly unexpected, especially if there's any gap at all between taking Algebra and taking Calc. The simple truth is, you forget material you don't use. And most people don't use a lot of algebra in their daily lives. If even a semester or two has passed since you took algebra, you're almost certainly going to have forgotten a lot of it, unless you made a very pointed effort to keep practicing that stuff and focus on retention.
I'm not sure I have any suggestion other than lots of practice. And know that you're not alone, this is a completely natural difficulty.