Question

What is the LCD of x+2/3=2x-4/2

Answer 1

Step-by-step explanation:

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Algebra

 

Find the LCD (3x)/(x-2) , 2/(x^2-4)

3xx−23xx-2 , 2x2−42x2-4

Simplify the denominator.

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3xx−2,2(x+2)(x−2)3xx-2,2(x+2)(x-2)

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

x−2,(x+2)(x−2)x-2,(x+2)(x-2)

The LCM is the smallest positive number that all of the numbers divide into evenly.

1. List the prime factors of each number.

2. Multiply each factor the greatest number of times it occurs in either number.

The number 11 is not a prime number because it only has one positive factor, which is itself.

Not prime

The LCM of 1,11,1 is the result of multiplying all prime factors the greatest number of times they occur in either number.

11

The factor for x−2x-2 is x−2x-2 itself.

(x−2)=x−2(x-2)=x-2

(x−2)(x-2) occurs 11 time.

The factor for x+2x+2 is x+2x+2 itself.

(x+2)=x+2(x+2)=x+2

(x+2)(x+2) occurs 11 time.

The factor for x−2x-2 is x−2x-2 itself.

(x−2)=x−2(x-2)=x-2

(x−2)(x-2) occurs 11 time.

Answer 2

We have to solve the question as

( x+2/3 )=(2x-4/2)

⇒((x+2)/3) - ((2x-4)/2) = 0

⇒ ($\frac{x+2}{3}$)= ( $\frac{2x-4}{2}$)

Now we can simplify right hand side and discard the 0 to get

( $\frac{x+2}{3}$) = (x-2)

⇒ (x+2 )= (3x-6)

Let,s subtract left side from right for:-

⇒(3x -x -6-2 )=0

⇒(2x - 8) = 0

⇒2x= 8

⇒x = $\frac{8}{2}$ = 4

Hence  x = 4

Ans :- x=4

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