Answer:
To simplify the expression (2 - 5√7) / (2 + 3√7) into the form a√7 + b, you can rationalize the denominator by multiplying both the numerator and denominator by the conjugate of the denominator, which is (2 - 3√7):
((2 - 5√7) / (2 + 3√7)) * ((2 - 3√7) / (2 - 3√7))
= (4 - 6√7 - 10√7 + 15√49) / (4 - 9*7)
= (4 - 16√7 + 15*7) / (4 - 63)
= (4 + 105 - 16√7) / (-59)
= (109 - 16√7) / (-59)
So, a = -16 and b = 109, giving the simplified form as -16√7 + 109.
