What is 3/8 x (_3/6)
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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).
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<h3><u>Solution:- </u></h3>
Let the number to be added be A
Now,
Transposing (−5x³+ 4x − 3 ) to other side-
Remember if there is a -ve sign before a bracket the signs of whole of the terms changes on opening bracket
Putting like terms together -
Therefore, 5x³+x²-5x +2 should be added to −5x³+ 4x − 3 to get x²− x − 1