Question

What is the least common denominator for the rational expressions 1 / x² -5 x-6} and 1/x²-12 x+36 ? Show your work.

Answer 1

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

$=\frac{1}{x^{2} -5x-6} , \frac{1}{x^{2} -12x+36}$  ...(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 ;

$=\frac{1}{(x+1)(x-6)} , \frac{1}{(x-6)(x-6)}$

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

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