The least common denominator for the rational expressions 1/x²-5x-6 and 1/x²-12 x+36 is (x-6)(x+1)(x-6).
In the given question
...(i)
First we will factor each denominator
So,
x²-5x-6
On splitting the factors of the above expression , we get
(x+1)(x-6) ....(ii)
x²-12x+36
On splitting the factors of the above expression , we get
(x-6)(x-6) ...(iii)
Substituting the value of (ii) and (iii) in (i) ,we get ;
As the LCM of denominator is the Least common denominator , we have
LCM of (x+1)(x-6) and (x-6)(x-6)
LCM=(x-6)(x+1)(x-6)
Hence the LCD is (x-6)(x+1)(x-6).
Therefore , the least common denominator for the rational expressions 1/x²-5x-6 and 1/x²-12 x+36 is (x-6)(x+1)(x-6).
Learn more about Least Common Denominator here brainly.com/question/11879136
#SPJ4
Given:
The given phrase is 16 seconds faster than Aya’s time.
To find:
The algebraic expression for the given phrase.
Solution:
Let x be the Aya’s time.
16 seconds faster than Aya’s time. It means 16 seconds less than Aya’s time.
We know that a negative sign "-" is used for less than.
16 seconds less than Aya’s time =
16 seconds faster than Aya’s time =
Therefore, the required algebraic expression is .