we can prove this by showing we can make the LHS and RHS look the same.

take the left hand side and multiply it by (which is 1, so you're not changing anything). simplify the expression

separately, take the right hand side, combine the fractions, then multiply by (which is 1, so you're not changing anything). simplify the expression and note that it is the same expression you got before when manipulating the left hand side. thus the equation is proved

now, how did i know what to multiply by?