I'm given the problem of finding the limit as x approaches 0 of tan3x/tan5x. To start, I replace tan with sin/cos, so that I get sin3x/cos3x/sin5x/cos5x. My professor wrote it out as sin3x/1 ⋅ 1/sin5x ⋅ cos5x ⋅ 1/cos3x. He then somehow found a way to get a 3x to the denominator of the first term after factoring out a 3/5, and add 5x to the numerator of the second term. I'm not sure how he managed that, could someone help me to understand?