divide 16xy2-21x2y+9x3-4y3 by x-y
Answers
Like multiplying rational expressions, dividing rational expressions follows the same basic rules as dividing fractions. When you divide two fractions, you turn the second fraction upside down as the first step, and then multiply. So:
(4 / 5) ÷ (3 / 2) = (4 / 5) × (2 / 3)
= (4 × 2) / (5 × 3)
= 8 / 15
Dividing two rational expressions works in the same way, so:
((x + 3) / 2_x_2) ÷ (4 / 3_x_) = ((x + 3) / 2_x_2) × (3_x_ / 4)
= ((x + 3) × 3_x_) / (2_x_2 × 4)
= (3_x_2 + 9_x_) / 8_x_2
This expression can be simplified, because there is a factor of x (including x2) in both terms in the numerator and a factor of x2 in the denominator. One set of _x_s can cancel to give:
(3_x_2 + 9_x_) / 8_x_2 = x(3_x_ + 9) / 8_x_2
= (3_x_ + 9) / 8_x_
You can only simplify expressions when you can remove a factor from the whole expression on the top and bottom as above. The following expression:
(x – 1) / x
Cannot be simplified in the same way because the x in the denominator divides the whole term in the numerator. You could write:
(x – 1) / x = (x / x) – (1 / x)
= 1 – (1 / x)
If you wanted to, though.