SOLUTION: I dont knw how to solve the equations and check them : help? My Teacher Gave me 50 probelms of these . i am only asking to do those so maybe after i knw how to do the rest of the 4

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Question 444212: I dont knw how to solve the equations and check them : help? My Teacher Gave me 50 probelms of these . i am only asking to do those so maybe after i knw how to do the rest of the 45 problems
1. x/2=x+1/4 --> have to solve and check I tryed to like elimate the bottom to like 2 because 2 can go into 4 so i thought the bottom woulve be 2 then i thought the top would be x^2+1 soo maybe the answer would be x^2+1/2?
2. 3/x-1=4/3x+2 ^^
3. 3x/x+1=0 ^^
4.3/x-1=1/x^2-1
Please Help me this is 75% of my grade AND its not even a test :(
Found 2 solutions by ewatrrr, Leaf W.:
Answer by ewatrrr(24785)   (Show Source): You can put this solution on YOUR website!
 

Hi

 1,2 and 4 Set Up for Cross Multiplying to solve:

   4x = 2(x+1)   2x = 2   x = 1

   3(3x+2) = 4(x-1)    5x = -10  x = -2



   3(x^2-1) = (x-1)

  3x^2 - x -2 = 0

factoring

 (3x+2)(x-1) = 0

 (3x+2)= 0   x = -2/3

  (x-1)= 0   x = 1



3. 3x/(x+1) = 0  x = 0 would work 

Answer by Leaf W.(135)   (Show Source): You can put this solution on YOUR website!
 1. 

Find the least common denominator (LCD) between 2 and 4... 4. Multiply the entire equation by this LCD: 

Simplify: 

Solve for x by subtracting x from both sides: 

Therefore, x = 1

2. 

Find the LCD between x-1 and 3x+2... (x-1)(3x+2) Multiply the entire equation by this LCD: 

Simplify (NOTE: the (x-1) and /(x-1) cancel each other out, and the same with the (3x+2) and /(3x+2)): 

Distribute: 

Subtract 6 from both sides: 

Subtract 4x from both sides: 

Divide both sides by 5: 

Therefore, x = -2

3. 

Since there is only one denominator, the LCD is x+1.



Simplify (NOTE: The (x+1) and /(x+1) cancel each other out, and 0 multiplied by anything is 0): 

Divide both sides by 3: 

Therefore, x = 0

4. 

Factor the denominator ( is a difference of squares, so (x+1)(x-1)): 

Find the LCD between x-1 and (x+1)(x-1)... (x+1)(x-1). Multiply the entire equation by this: 

Simplify: 

Distribute: 

Subtract 3 from both sides: 

Divide both sides by 3: 

Therefore,  

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