Answer:
(i) To simplify (b²-a²) ÷ (2a²+ab-3b²), we can factor the numerator and denominator using the difference of squares formula, which states that a² - b² = (a + b)(a - b).
(b²-a²) = (b + a)(b - a)
(2a²+ab-3b²) = (2a-b)(a+3b)
Thus, we can rewrite the expression as:
(b + a)(b - a) / (2a-b)(a+3b)
(ii) To simplify (3x-3y) ÷ (ax-ay-x+y), we can factor out the common factor of 3 from the numerator and the common factor of (a-1) from the denominator:
3(x-y) / (a-1)(x-y)
We can then cancel the common factor of (x-y) to get the simplified form:
3 / a-1
(iii) To simplify (y²-6y-7) ÷ (2y²-17y+21), we can factor both the numerator and the denominator:
(y-7)(y+1) / (2y-3)(y-7)
We can then cancel out the common factor of (y-7) to get the simplified form:
(y+1) / (2y-3)
(iv) To simplify (a²-ab-ac+bc) ÷ (a²+ab-ac-bc), we can factor out the -1 from the denominator:
(a²-ab-ac+bc) ÷ -1(a²-ab+ac-bc)
We can then factor out the common factor of (a-b) from both the numerator and the denominator:
(a-b)(a-c) ÷ -1(a-b)(a+c)
Cancelling out the common factor of (a-b) gives us the simplified expression:
(c-a) / (a+c)