how do I solve
(4x^2-9y^2)/2x+3y)
a^2-b^2 = (a-b)(a+b)
(2x-3y)(2x+3y)/(2x+3y)
2x-3y
How do I find the quotient of:
4x^2-9y^2 / 2x+3y
To solve the expression (4x^2 - 9y^2) / (2x + 3y), we can simplify it by factoring the numerator and denominator and then canceling out any common factors.
Step 1: Factor the numerator. The numerator is a difference of squares, so we can use the formula a^2 - b^2 = (a + b)(a - b). Applying this formula, we have:
4x^2 - 9y^2 = (2x + 3y)(2x - 3y)
Step 2: Factor the denominator. Since the denominator doesn't easily factor further, we can skip this step.
Step 3: Cancel out common factors. Since the numerator and denominator have a common factor of (2x + 3y), we can cancel it out from both sides of the expression:
[(2x + 3y)(2x - 3y)] / (2x + 3y)
After canceling out the common factor, we're left with the simplified expression (2x - 3y). Therefore, the solution to the expression (4x^2 - 9y^2) / (2x + 3y) is (2x - 3y).