# 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(1539)   (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.