Question

Which of the following pairs of rational algebraic expressions have a(a-2) as their LCD?

A. 1/a+2 and a/a²-4
B. 1/2a and a/a²+3a+2
C. 1/a+2 and a/a-2
D. 1/a²-2a and a/a-2

Answer 1

To find the pair of rational algebraic expressions that have a(a-2) as their least common denominator (LCD), we need to factor the expressions and identify their common factors.

Step-by-step explanation:

To find the pair of rational algebraic expressions that have a(a-2) as their least common denominator (LCD), we need to factor the expressions and identify their common factors.

Factoring a(a-2), we get a²-2a.

A. The expression 1/a+2 can be simplified to 1/(a+2). The expression a/a²-4 can be simplified to a/(a+2)(a-2). The LCD is a(a-2), so the correct pair is A.

B. The expression 1/2a can be simplified to 1/(2a). The expression a/a²+3a+2 cannot be simplified. The LCD is a(a-2), so the pair is not B.

C. The expression 1/a+2 can be simplified to 1/(a+2). The expression a/a-2 can be simplified to a/(a-2). The LCD is a(a-2), so the correct pair is C.

D. The expression 1/a²-2a cannot be simplified. The expression a/a-2 can be simplified to 1/(a-2). The LCD is a(a-2), so the pair is not D.