1 over x squared minus 1 over y squared divided by 1 over y plus 1 over x

Question

in simplest form, 1/x squared - 1/y squared over 1/y + 1/x is equivalent to

Answer 1

1 over x squared minus 1 over y squared divided by 1 over y plus 1 over x

in simplest form, 1/x^2 - 1/y^2

                            1/y + 1/x 

get common denominators

y^2 - x^2

x^2y^2       

x + y

xy

now flip the bottom and multiply

y^2 - x^2  *      xy    

x^2y^2         y + x

(y + x)(y - x)

xy(y + x)

y - x

xy

Answer 2

The arithmetic average of two numbers x and y is

StartFraction x plus y Over 2 EndFractionx+y2.

Use deductive reasoning to explain why if three numbers​ a, b, and c form an arithmetic​ sequence, then b is the arithmetic average of a and c.