Factor and reduce to simplest form.6x2 + 11xy − 10y23x2 + 10xy − 8y2

First, let's factor each of the two expressions separately.

For the first expression, 6x^2 + 11xy - 10y^2, we are looking for two numbers that multiply to (6*-10)=-60 and add to 11. Those numbers are 15 and -4. So we can rewrite the expression as:

6x^2 + 15xy - 4xy - 10y^2

Now, we can factor by grouping:

3x(2x + 5y) - 2y(2x + 5y)

So the factored form of the first expression is (3x - 2y)(2x + 5y).

For the second expression, 3x^2 + 10xy - 8y^2, we are looking for two numbers that multiply to (3*-8)=-24 and add to 10. Those numbers are 12 and -2. So we can rewrite the expression as:

3x^2 + 12xy - 2xy - 8y^2

Now, we can factor by grouping:

x(3x + 4y) - 2y(3x + 4y)

So the factored form of the second expression is (x - 2y)(3x + 4y).

Therefore, the factored form of the entire expression is:

(3x - 2y)(2x + 5y) / (x - 2y)(3x + 4y)

We can see that (3x - 2y) is a common factor in the numerator and the denominator, so we can cancel it out to reduce the expression to simplest form:

(2x + 5y) / (3x + 4y)