SOLUTION: how do you do this problem? 1/a + 2/b = 3/c Solve for b. I have tired my brain out trying to solve this problem!! Thanks!!

Algebra ->  Equations -> SOLUTION: how do you do this problem? 1/a + 2/b = 3/c Solve for b. I have tired my brain out trying to solve this problem!! Thanks!!      Log On


   

Question 51395: how do you do this problem? 1/a + 2/b = 3/c Solve for b. I have tired my brain out trying to solve this problem!! Thanks!!
Found 2 solutions by Earlsdon, rchill:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Ok. give your brain a rest and let's see what can be done with this:
Solve:
1%2Fa+%2B+2%2Fb+=+3%2Fc for b. First, subtract 1%2Fa from both sides.
2%2Fb+=+3%2Fc+-+1%2Fa Now combine the two fractions on right side.
2%2Fb+=+%283a-c%29%2Fac Next, multiply both sides by ac
2ac%2Fb+=+3a-c Then multiply both sides by b
2ac+=+b%283a-c%29 Finally, divide both sides by (3a-c)
2ac%2F%283a-c%29+=+b
So, b+=+2ac%2F%283a-c%29

Answer by rchill(405) About Me  (Show Source):
You can put this solution on YOUR website!
You need to isolate b to solve for b. To do this, because the left side of the equation is addition, you need to subtract +1%2Fa+ from both sides of the equation. The equation becomes +1%2Fa+%2B+2%2Fb+-+1%2Fa+=+3%2Fc+-+1%2Fa+, which reduces down to +2%2Fb+=+3%2Fc+-+1%2Fa+. Now that b has been isolated to itself on the left side of the equation (i.e., +2%2Fb+), and because +3%2Fc+-+1%2Fa+ is the same as saying +%283%2Fc+-+1%2Fa%29+%2F+1+, we can cross multiply. This means we multiply the left side numerator (i.e., 2) by the right side denominator (i.e., 1) and set that equal to the left side denominator (i.e., b) multiplied by the right side numerator (i.e., +3%2Fc+-+1%2Fa+). The new equation becomes +2%2A1+=+b%2A%283%2Fc+-+1%2Fa%29+, which simplifies to +2+=+b%2A%283%2Fc+-+1%2Fa%29+. Dividing both sides by +3%2Fc+-+1%2Fa+ produces +2+%2F+%283%2Fc+-+1%2Fa%29+=+%28b%2A%283%2Fc+-+1%2Fa%29%29+%2F+%283%2Fc+-+1%2Fa%29+. This equation simplifies to +2+%2F+%283%2Fc+-+1%2Fa%29+=+b+, and thus is the answer. To check our answer, we substitute it into the original equation for b, producing +1%2Fa+%2B+2%2F%282+%2F+%283%2Fc+-+1%2Fa%29%29+=+3%2Fc+. Now subtract +1%2Fa+ from both sides, producing +2%2F%282+%2F+%283%2Fc+-+1%2Fa%29%29+=+3%2Fc+-+1%2Fa+. Now multiply both sides by +2+%2F+%283%2Fc+-+1%2Fa%29+ and you'll get 2=2, which is a true statement, and that means our answer is correct.