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
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
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.
