find the LCD for the list of rational expressions.?

Question

find the LCD for the list of rational expressions. 2 / 2x+6 , 15 / 2x^2 + 12x +18


Im having a bit of trouble with this one, thanks for any help!

Answer 1

2/(2x+6) = 1/(x+3)



15(2x^2+12x+18)=15/[2(x+3)^2]



x+3 is included in the second equation



So, the LCD is 2(x+3)^2

Answer 2

You need to factorize..

you will get..

2x+6 = 2*(x+3)

2x^2 + 12x +18 = 2*(x+3)^2



You have two approaches here..



1. Calculate LCDs for numerator and denominator separately.

Dont cancel the 2's in the first expression. [because 2 is a common factor in denominators for the expressions]

You have the expressions, 2 / 2*(x+3) and 15 / 2*(x+3)^2

Now since 2 and 15 have no factor in common, the LCD for numerators would be 2*15 = 30..

And the denominators have 2 and (x+3) as a common factor, their LCD would be (2*(x+3)^2) [you dont multiply 2 and (x+3) two times, because they are common factors]



Hence, the answer would be,

30 / (2*(x+3)^2) = 15 / (x+3)^2



2. Calculate the LCDs for constants and expressions of x seperately.

Cancel the 2's in the first expression.

You have the expressions, 1 / (x+3) and 15 / 2*(x+3)^2

Now the constants in the two expressions are 1 and 15/2, and there LCD = 15

[ how?

what are the multiples of 15/2? 15/2, 30/2=15, 45/2, 60/2=30,....

and multiples of 1 are 1, 2, 3,..., 14, 15,16,...

which is is the least common multiple for both the numbers? 15 ]

Now in the expressions (without constants) 1/ (x+3) and 1 / (x+3)^2 the common factor is 1 / (x+3)

so LCD for them is 1 / (x+3)^2.

Multiply the LCDs for constants and expressions to get the final answer 15 / (x+3)^2

Answer 3

1/(x + 3), 15/2*(x + 3)^2



lcd = 2*(x + 3)^2

Answer 4

3x +3 = 3(x+a million) ................(a million) 2x^2 + 4x + 2 =2(x^2 + 2x + a million) =2((x+a million)^2 ......................(2) from (a million) and (2), (x+a million) is the bottom elementary aspect that is the liquid crystal demonstrate(lowest elementary divisor)