Question 206452
There are two ways to solve this:


Method #1


{{{1/a + 1/b = c}}} Start with the given equation.



{{{b/(ab) + 1/b = c}}} Multiply the first fraction by {{{b/b}}}



{{{b/(ab) +a/(ab) = c}}} Multiply the second fraction by {{{a/a}}}



{{{(b+a)/(ab) = c}}} Add the fractions.



{{{b+a = cab}}} Multiply both sides by ab.



{{{b = cab-a}}} Subtract 'a' from both sides.



{{{b - cab=-a}}} Subtract cab from both sides.



{{{b(1 - ca)=-a}}} Factor out the GCF 'b' from the left side.



{{{b=-a/(1 - ca)}}} Divide both sides by 1 - ca.



So the solution is {{{b=-a/(1 - ca)}}}



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OR....


Method #2


{{{1/a + 1/b = c}}} Start with the given equation.



{{{cross(a)b(1/cross(a)) + a*cross(b)(1/cross(b)) = cab}}} Multiply EVERY term by the LCD 'ab' to clear out the fractions.


{{{b+a=cab}}} Multiply and simplify



{{{b = cab-a}}} Subtract 'a' from both sides.



{{{b - cab=-a}}} Subtract cab from both sides.



{{{b(1 - ca)=-a}}} Factor out the GCF 'b' from the left side.



{{{b=-a/(1 - ca)}}} Divide both sides by 1 - ca.



So the solution is (once again) {{{b=-a/(1 - ca)}}}



Note: your book may simplify the final answer to go from {{{b=-a/(1 - ca)}}} to {{{b=-a/(-1(-1 + ca))}}} to {{{b=a/(-1 + ca)}}} to {{{b=a/(ca-1)}}} (and possibly to {{{b=a/(ac-1)}}}). So just keep in mind that there are many ways to state the final answer.