Question

The lcd of 1/a²-1 and 1/a²+1

Answer 1

Step-by-step explanation:

We know that the least common multiple (LCM) is the smallest number or expression that is a common multiple of two or more numbers or algebraic terms.

We first factorize the given binomials 3(a−1),2(a−1)

2

and a

2

−1 as shown below:

3(a−1)=3×(a−1)

2(a−1)

2

=2×(a−1)×(a−1)

a

2

−1=a

2

−1

2

=(a−1)×(a+1)(∵x

2

−y

2

=(x−y)(x+y))

Now multiply all the factors, using each common factor only once, therefore, the LCM is:

3×2×(a−1)×(a−1)×(a+1)=6(a−1)

2

(a+1)

Hence, the LCM of 3(a−1),2(a−1)

2

and a

2

−1 is 6(a−1)

2

(a+1)