8 / (x - y)² ÷ 12 / (x² - y²)
= 8 / (x - y)² · (x² - y²) / 12
= [ 8 · (x² - y²) ] / [ (x - y)² · 12 ]
= [ 8 · (x + y)(x - y) ] / [ (x - y)(x - y) · 12 ]
Reduce 8/12 = 2/3 and cancel the factors (x - y) from the numerator and denominator:
= [ 2 · (x + y) ] / [ 3 · (x - y) ]