To multiply the rational expressions, we first need to factor each expression:
The numerator of the first rational expression, x^2 + 2x -3, factors to (x + 3)(x - 1).
The denominator of the first rational expression, x^2 + 3x - 4, factors to (x + 4)(x - 1).
The numerator of the second rational expression, x^2 + 6x +8, factors to (x + 2)(x + 4).
The denominator of the second rational expression, x^2 - 9, factors to (x - 3)(x + 3).
Next, we can cancel out some common factors:
(x + 3)(x - 1)/(x + 4)(x - 1) * (x + 2)(x + 4)/(x - 3)(x + 3)
The (x - 1) term in the numerator and denominator cancels out.
(x + 3)/(x + 4) * (x + 2)(x + 4)/(x - 3)
Now, we can multiply the numerators and denominators:
(x + 3)(x + 2)(x + 4)/(x + 4)(x - 3)
The (x + 4) term in the numerator and denominator cancels out.
(x + 3)(x + 2)/(x - 3)
So, the product of the rational expressions, in simplest form, is (x + 3)(x + 2)/(x - 3). Therefore, the correct answer is option 3.
Multiply the rational expression and write the product in simplest form: x^2+2x−3/x^2+3x−4 ⋅ x^2+6x+8/x^2−9 .(1 point)
1. -2/3
2. (x+4)(x+2)/(x+3)(x-3)
3. x+2/x-3
4. -(x+2)/x+3
1 answer
1 answer