Question

1/a + 1/b + 1/c = 1/x

Solve for x

Answer 1

x=
`(abc)/((bc+ac+ab))`

Explanation:

First, we need to remove the fractions on the left hand side, which we can do by multiplying each term by the lowest common multiple of the denominators. Since the denominators are all different (a,b and c), then the lowest common multiple is just all three multiplied together: abc

So, our original equation:

`(1)/(a)+(1)/(b)+(1)/(c)=(1)/(x)` now becomes:

`(abc)/(a)+(abc)/(b)+(abc)/(c)=(abc)/(x)`

Now we can simplify the fractions on the right hand side because each numerator can now be divided by its denominator:

`bc+ac+ab=(abc)/(x)`

Now we can just rearrange the equation to solve for x by replacing the x with (bc+ac+ab), because if abc/x= bc+ac+ab, then abc/bc+ac+ab=x, as x and bc+ac+ab multiply to abc:

`x(bc+ac+ab)=abc`

`x=(abc)/(bc+ac+ab)`

Hope this helped!