Question

Rewrite the following rational expressions as equivalent expressions with the denominator (x+3)(x – 4)(x +4):

a)2/x^2-x-12
b)1/x^2-16
A) 2/(x+3)(x-4)(x+4)} ),1/(x+3)(x-4)(x+4)
B)2/(x-3)(x+4)(x+4)} ),1/(x-3)(x+4)(x+4)
C)2/(x+3)(x-4)} ),1/(x+4)(x-4)
D)2/(x+3)(x-4)(x+4)} ),1/(x-4)(x+4)

Answer 1

To rewrite the rational expressions with the given denominator, we need to factor the denominators of the expressions and write them with the common denominator. For expression a, the rewritten form is (2x+8)/((x-4)(x+3)(x+4)). For expression b, the rewritten form is 1/((x-4)(x+3)(x+4)).

Step-by-step explanation:

To rewrite the rational expressions, we need to factor the denominators of the given expressions and write them with the common denominator (x+3)(x-4)(x+4).

a) For the expression 2/x^2-x-12, we first factor the denominator as (x-4)(x+3). Now, we can rewrite the expression as 2/((x-4)(x+3)) * ((x+4)/(x+4)) = 2(x+4)/((x-4)(x+3)(x+4)) = (2x+8)/((x-4)(x+3)(x+4)).

b) For the expression 1/x^2-16, we factor the denominator as (x-4)(x+4). We rewrite the expression as 1/((x-4)(x+4)) = 1/((x-4)(x+3)(x+4)).