Multiply the rational expression and write the product in simplest form: x2+2x−3x2+3x−4⋅x2+6x+8x2−9 .(1 point)
Responses
−23
negative Start Fraction 2 over 3 End Fraction
(x+4)(x+2)(x+3)(x−3)
Start Fraction left parenthesis x plus 4 right parenthesis left parenthesis x plus 2 right parenthesis over left parenthesis x plus 3 right parenthesis left parenthesis x minus 3 right parenthesis End Fraction
−(x+2)x+3
Start Fraction negative left parenthesis x plus 2 right parenthesis over x plus 3 End Fraction
x+2x−3
The correct answer is: (x+2)(x-3)
To multiply the rational expression and write the product in simplest form, follow these steps:
Step 1: Factor the numerators and denominators of both rational expressions.
The first rational expression, x^2+2x−3, can be factored as (x+3)(x-1).
The second rational expression, x^2+6x+8x^2−9, can be factored as (x+3)(x-1).
Step 2: Cancel out common factors from the numerators and denominators.
Since both numerators and denominators have the common factor (x+3)(x-1), we can cancel it out.
Step 3: Multiply the remaining factors.
After canceling out the common factors, the product of the rational expressions is (x+3)(x-1).
So, the product in simplest form is (x+3)(x-1).
To multiply rational expressions and write the product in simplest form, you need to follow these steps:
1. Factor both the numerator and denominator if they are not already factored.
2. Cancel out any common factors between the numerator and denominator.
3. Multiply the remaining factors in the numerator and denominator.
4. Simplify the resulting expression by performing any necessary operations, such as combining like terms or simplifying fractions.
Let's apply these steps to the given rational expression: (x^2 + 2x - 3)/(x^2 + 3x - 4) * (x^2 + 6x + 8)/(x^2 - 9).
1. Factor the numerator and denominator if needed:
The numerator can be factored as (x+3)(x-1) and the denominator can be factored as (x+4)(x-1).
2. Cancel out any common factors:
In this case, we have a common factor of (x-1) in both the numerator and the denominator. Canceling it out, we are left with (x+3)/(x+4).
3. Multiply the remaining factors:
Multiply (x+3) and (x+4), resulting in (x+3)(x+4).
4. Simplify the expression, if possible:
Since no further simplification can be done, the final product is (x+3)(x+4).
Thus, the answer to the question is (x+3)(x+4).