All it asks is to simplify the results.
1-9a^2/a+1 divided by 4x^2-y^2/x+y
To simplify the given expression (1-9a^2)/(a+1) divided by (4x^2-y^2)/(x+y), we need to simplify each expression separately and then divide them.
Let's start with the expression (1-9a^2)/(a+1).
To simplify this expression, we can use the difference of squares formula, which states that a^2 - b^2 = (a+b)(a-b).
Here, we have 1 - 9a^2, which can be recognized as a difference of squares: (1)^2 - (3a)^2.
Using the difference of squares formula, we can rewrite it as:
(1 - 3a)(1 + 3a).
Next, let's simplify the expression (4x^2-y^2)/(x+y).
This expression can be recognized as a difference of squares as well: (2x)^2 - y^2.
Using the difference of squares formula, we can rewrite it as:
(2x - y)(2x + y).
Now, we can divide the two simplified expressions:
[(1 - 3a)(1 + 3a)] / [(2x - y)(2x + y)].
Remember that division can be simplified by multiplying by the reciprocal. So, we can rewrite the expression as:
[(1 - 3a)(1 + 3a)] * [(2x + y)/(2x - y)].
So, the simplified result is [(1 - 3a)(1 + 3a)] * [(2x + y)/(2x - y)].