Verify this equation only working on the left side

   

one strategy is to combine fractions.

if we want to add fractions, we need a common denominator.

if we multiply the numerator and denominator of  by  and multiply the numerator and denominator of  by  , then we will get a common denominator of 

   

distribute the 

   

and  are like terms and cancel each other out

   

the denominator can be expanded.

difference of squares:  

   

therefore

   

we have a variant of the pythagorean identity that we can use here.

if 

   

then subtracting both sides by  gets us

   

we can substitute this

   

by definition,