simplify:
12x^2 + 8x
-------------
9x^2 - 4
12x^2+8x = 4x(3x+2)
9x^2-4 = (3x-2)(3x+2)
I think you can see which factor cancels.
thank you!
To simplify the fraction (also known as rational expression) 12x^2 + 8x / 9x^2 - 4, we can factor both the numerator and the denominator, and then cancel out any common factors.
Let's start by factoring the numerator and denominator separately:
Numerator: 12x^2 + 8x
Taking out the greatest common factor of both terms, which is 4x:
4x(3x + 2)
Denominator: 9x^2 - 4
This is a difference of squares, and can be factored as:
(3x + 2)(3x - 2)
Now that we have factored both the numerator and denominator, we can rewrite the expression as:
[4x(3x + 2)] / [(3x + 2)(3x - 2)]
Next, we can see that there is a common factor of (3x + 2) in both the numerator and denominator. We can cancel them out:
[4x(3x + 2)] / [(3x + 2)(3x - 2)] = 4x / (3x - 2)
Therefore, the simplified form of the fraction 12x^2 + 8x / 9x^2 - 4 is 4x / (3x - 2).