Question

Please helppp me with this. 20 pointsss

Answer 1

(a-6) (a-1) (a+6)

Explanation:

Factor the first denominator

(a^2 -7a+6)

What 2 numbers multiply together to give us 6 and add together to give us -7

-6*-1 = 6

-6+-1 = -7

(a-6) (a-1)

Factor the second denominator

a^2 - 36

This is the difference of squares

(a-6) (a+6)

We need the LCD or leas common denominator

Look at each term and put it in the denominator the least number of times it appears

(a-6) (a-1) (a+6)

This is the least common denominator

Answer 2

`\large\boxed{LCD=(a-1)(a-6)(a+6)}`

Explanation:

`(6)/(a^2-7a+6)=(6)/(a^2-a-6a+6)=(6)/(a(a-1)-6(a-1))\\\\=(6)/((a-1)(a-6))\\--------------------------\\(3)/(a^2-36)\qquad\text{use}\ x^2-y^2-(x-y)(x+y)\\\\=(3)/(a^2-6^2)=(3)/((a-6)(a+6))\\\\LCD=(a-1)(a-6)(a+6)`