Answer :

For carrying out divisions we will take common factors from numerator and denominator and then cancel out the common factors.**For Example:**

In this example (a - b) as common in both numerator and denominator get cancelled out.

(i) (10x - 25)÷(5)

Common factor of 10x - 25 = 5

Now, as 5 is common, it get cancelled out from numerator and denominator.

(ii) (10x - 25)÷(2x - 5)

Now, we can write the denominator as,

Now, clearly (2x - 5) is common in both numerator and denominator. Therefore, it get cancelled out.

(iii) 10y(6y + 21)÷5(2y + 7)

We can write the numerator as,

Now, Clearly 5(2y + 7) is common in both numerator and denominator and therefore it gets cancelled out.

Hence,

10y(6y + 21)÷5(2y + 7) = 6y

(iv) **9x ^{2} y^{2} (3z - 24)÷27xy(z - 8)**

Now, we can write the given division as,

From above we can see that, 27xy(z - 8) is common in both numerator and denominator and so it gets cancelled out.

**Hence, 9x ^{2} y^{2} (3z - 24)÷27xy(z - 8) = xy**

(v) 96abc (3a - 12)(5b - 30) ÷ 144 (a - 4)(b - 6)

We can write the given division as,From above we can see that,

144(a - 4)(b - 6) is common in both numerator and denominator and so gets cancelled out.

**Hence, 96abc (3a - 12)(5b - 30) ÷ 144 (a - 4)(b - 6) = 10abc**

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