Question 464194: Hello,
I think I know how to do problems like these, but I always seem to get problems like this one wrong. Can you help me solve this one? Then maybe I can figure out what I'm doing wrong.
Here's the problem:
3/y+2 + 4/y-3 = 7/y+6
Thanks.
Sarah
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! 3/y+2 + 4/y-3 = 7/y+6
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The first step to solving these problems is to find the lowest common denominator or LCD. Notice that in given problem there is nothing common with the three denominators, so the LCD must include all three denominators, that is,LCD = (y+2)(y-3)(y+6).
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The next step is to multiply each of the three terms by the LCD, like so:
for first term: 3/(y+2)* (y+2)(y-3)(y+6)=3(y-3)(y+6) (notice how (y+2) drops out)
for 2nd term: 4/(y-3)* (y+2)(y-3)(y+6)=4(y+2)(y+6) (notice how (y-3) drops out)
for 3rd term: 7/(y+6)* (y+2)(y-3)(y+6)=7(y-3)(y+2) (notice how (y+6) drops out)
putting back into equation form:
3(y-3)(y+6)+4(y+2)(y+6)=7(y-3)(y+2)
notice now you don't have denominators to work with.
from hereon in, expand (distribute) and combine like terms:
3(y^2+3y-18)+4(y^2+8y+12)=7(y^2-y-6)
3y^2+9y-54+4y^2+32y+48=7y^2-7y-42
7y^2+41y-6=7y^2-7y-42
48y=-36
y=36/48=-3/4=-.75
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Check:
3/y+2 + 4/y-3 = 7/y+6
3/1.25+4/-3.75=7/5.25
2.4-1.0667=1.333
1.333=1.333
comment: you need to be patient and very careful when working with such problems
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