Question 41476
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:
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(12)(2x+1)/3 + (12)(x-2)/4 - (12)(x-3)/6 + (12)(5-x)/2
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Cancel within the numerator where ever possible:
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[(4)2x+1)+ (3)(x-2)-(2)(x-3)+ (6)(5-x)]/12
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Simplify by multiplying
[(4)(2x+1)+ (3)(x-2)-(2)(x-3)+(6)(5-x)]/12
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[8x+4+3x-6-2x+6+30-6x]/12
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Simplify by combining like terms (add or subtract):
[8x+4+3x-6-2x+6+30-6x]/12
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[3x+34]/12 which cannot be simplified nor reduced any further.