Question

Question #d7fa5

Answer 1

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

Explanation:

One way of solving the equation for X is to express the right side as a single fraction.

To do this we require the fractions to have a `color(blue)"common denominator"`

This requires the `color(blue)"lowest common multiple"` (LCM) of the denominators a , b and c

The LCM of a, b and c is abc

Each fraction has one factor of abc on the denominator so multiplying numerator/denominator by the product of the other 2 factors will give the common denominator required.

`rArr1/axxcolor(red)((bc)/(bc))+1/bxxcolor(blue)((ac)/(ac))+1/cxxcolor(magenta)((ab)/(ab))`

`=(bc)/(abc)+(ac)/(abc)+(ab)/(abc)larr" common denominator"`

We can now add the numerators, leaving the denominator.

`rArr1/X=(bc+ac+ab)/(abc)`

To solve for X, either `color(blue)"cross-multiply"` or `color(red)"invert"` both sides of the equation.

cross-multiplying gives.

`X(bc+ac+ab)=1xxabc=abc`

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