Question

Someone please do this problem for me.​

Answer 1

Given:

$\frac{6}{a^{2}-7 a+6}, \frac{3}{a^{2}-36}$

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).