6x(squared) - 2xy
________________________ (divided by)
y(squared) - 9x(squared)
factor out of the numerator -2x, so that
-2x(y-3x) is the numerator.
Factor the denominator as the difference of squares.
How do i do the difference os quares if y and 9x are different.
(a^2-b^2)=(a-b)(a+b) YOU should have memorized that.
To simplify the expression (6x^2 - 2xy) divided by (y^2 - 9x^2), we can factor both the numerator and the denominator and then cancel out any common factors.
Let's start by factoring the numerator:
6x^2 - 2xy
We can factor out the common factor of 2x:
2x(3x - y)
Now, let's factor the denominator:
y^2 - 9x^2
This is a difference of squares, so we can rewrite it as:
(y + 3x)(y - 3x)
Now, the expression becomes:
(2x(3x - y)) / ((y + 3x)(y - 3x))
Next, we can cancel out any common factors between the numerator and the denominator. In this case, both the numerator and the denominator have a factor of (3x - y), so we can cancel it out:
(2x * 1) / ((y + 3x)(y - 3x))
Finally, we have simplified the expression to:
(2x) / ((y + 3x)(y - 3x))
So, the simplified form of the expression (6x^2 - 2xy) divided by (y^2 - 9x^2) is (2x) / ((y + 3x)(y - 3x)).