SOLUTION: 1/a + 1/b = c for b how do I work this?

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Question 206452This question is from textbook elementary & intermediate algebra
: 1/a + 1/b = c for b how do I work this?
 This question is from textbook elementary & intermediate algebra

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
There are two ways to solve this:

Method #1

1%2Fa+%2B+1%2Fb+=+c Start with the given equation.


b%2F%28ab%29+%2B+1%2Fb+=+c Multiply the first fraction by b%2Fb


b%2F%28ab%29+%2Ba%2F%28ab%29+=+c Multiply the second fraction by a%2Fa


%28b%2Ba%29%2F%28ab%29+=+c Add the fractions.


b%2Ba+=+cab Multiply both sides by ab.


b+=+cab-a Subtract 'a' from both sides.


b+-+cab=-a Subtract cab from both sides.


b%281+-+ca%29=-a Factor out the GCF 'b' from the left side.


b=-a%2F%281+-+ca%29 Divide both sides by 1 - ca.


So the solution is b=-a%2F%281+-+ca%29


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OR....

Method #2

1%2Fa+%2B+1%2Fb+=+c Start with the given equation.


cross%28a%29b%281%2Fcross%28a%29%29+%2B+a%2Across%28b%29%281%2Fcross%28b%29%29+=+cab Multiply EVERY term by the LCD 'ab' to clear out the fractions.

b%2Ba=cab Multiply and simplify


b+=+cab-a Subtract 'a' from both sides.


b+-+cab=-a Subtract cab from both sides.


b%281+-+ca%29=-a Factor out the GCF 'b' from the left side.


b=-a%2F%281+-+ca%29 Divide both sides by 1 - ca.


So the solution is (once again) b=-a%2F%281+-+ca%29


Note: your book may simplify the final answer to go from b=-a%2F%281+-+ca%29 to b=-a%2F%28-1%28-1+%2B+ca%29%29 to b=a%2F%28-1+%2B+ca%29 to b=a%2F%28ca-1%29 (and possibly to b=a%2F%28ac-1%29). So just keep in mind that there are many ways to state the final answer.