Question

Someone please do this problem for me.​

Answer 1

Given:

`$(6)/(a^(2)-7 a+6), (3)/(a^(2)-36)`

To find:

The LCD of the fractions.

Solution:

LCD means least common denominator.

Let us find the least common multiplier for the denominator.

The denominators are
`\left(a^(2)-7 a+a\right),\left(a^(2)-36\right)`.

Factor
`\left(a^(2)-7 a+a\right)`:

`a^(2)-7 a+6=\left(a^(2)-a\right)+(-6 a+6)`

Take a common in first 2 terms and -6 common in next two terms.

`=a(a-1)-6(a-1)`

Take out common factor (a - 1).

`\left(a^(2)-7 a+a\right)=(a-1)(a-6)` ------------- (1)

Factor
`\left(a^(2)-36\right)`:

`\left(a^(2)-36\right)=\left(a^(2)-6^2\right)`

Using identity:
`(a^2-b^2)=(a-b)(a+b)`

`\left(a^(2)-36\right)=(a-6)(a+6)` ------------- (1)

From (1) and (2),

LCM of
`\left(a^(2)-7 a+a\right),\left(a^(2)-36\right)=(a-1)(a-6)(a+6)`

Therefore LCD is (a - 1)(a - 6)(a + 6).