I began working on this problem this morning, and my calc equations kept getting bigger and bigger, then after I had about 2 pages filled with equations, I saw

I began working on this problem this morning, and my calc equations kept getting bigger and bigger, then after I had about 2 pages filled with equations, I saw your post. I feel much better now knowing I wasn't missing something obvious, and I can finally move onto my actual work for the morning after seeing the solutions. Thanks!