SOLUTION: i was wondering how to add (2x+1)+(x-2)-(x-3)+(5-x) ---- ---- ---- ---- 3 4 6 2 the answer is 3x

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Question 41476: i was wondering how to add (2x+1)+(x-2)-(x-3)+(5-x)
---- ---- ---- ----
3 4 6 2
the answer is 3x+34
------
12 but i dont know how to get that answer
Found 2 solutions by AnlytcPhil, tutorcecilia:
Answer by AnlytcPhil(1806)   (Show Source): You can put this solution on YOUR website!
I was wondering how to add      

2x+1   x-2   x-3   5-x
———— + ——— - ——— + ———                           
 3      4     6     2       

the answer is 

3x+34
—————
 12

The LCD of 3, 4, 6, and 2 is 12.  So we:

Multiply the first fraction by (4)/(4) to 
make it have a denominator of 12

(4)(2x+1)     8x+4  
——————————  = ————                          
  (4)3         12

Multiply the second fraction by (3)/(3) to 
make it have a denominator of 12

(3)(x-2)     3x-6  
—————————  = ————                          
  (3)4        12

Multiply the third fraction by (2)/(2) to 
make it have a denominator of 12

  (2)(x-3)       2x-6  
- —————————  = - ————                          
    (2)6          12

Multiply the fourth fraction by (6)/(6) to 
make it have a denominator of 12

(6)(5-x)     30-6x  
—————————  = —————                          
  (6)2        12

So the original expression

2x+1   x-2   x-3   5-x
———— + ——— - ——— + ———                           
 3      4     6     2 

becomes

8x+4   3x-6   2x-6   30-6x
———— + ———— - ———— + —————                           
 12     12     12      12

Enclose the numerators in paretheses, so we
won't get the signs wrong:

(8x+4)   (3x-6)   (2x-6)   (30-6x)
—————— + —————— - —————— + ———————                           
  12       12       12       12

Combine the numerators over the LCD of 12,
using the signs of the fractions:

(8x+4)+(3x-6)-(2x-6)+(30-6x)
————————————————————————————  
            12

Remove the parentheses

8x+4+3x-6-2x+6+30-6x
————————————————————  
         12

Get like terms together in the numerator

8x+3x-2x-6x+4-6+6+30
————————————————————  
         12

Combine the like terms:

3x + 34
———————
  12

Edwin
AnlytcPhil@aol.com
Answer by tutorcecilia(2152)   (Show Source): You can put this solution on YOUR website!
Find the least common denominator (LCD). Multiply each fraction by the LCD and cancel or reduce wherever possible. Combine like-terms within the numerator.
The LCD in this problem is 12 because each denominator divides 12 evenly.
Multiply each fraction by 12:
.
(12)(2x+1)/3 + (12)(x-2)/4 - (12)(x-3)/6 + (12)(5-x)/2
.
.
Cancel within the numerator where ever possible:
.
[(4)2x+1)+ (3)(x-2)-(2)(x-3)+ (6)(5-x)]/12
.
.
Simplify by multiplying
[(4)(2x+1)+ (3)(x-2)-(2)(x-3)+(6)(5-x)]/12
.
.
[8x+4+3x-6-2x+6+30-6x]/12
.
.
Simplify by combining like terms (add or subtract):
[8x+4+3x-6-2x+6+30-6x]/12
.
.
[3x+34]/12 which cannot be simplified nor reduced any further.
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