Question

How do you solve `\frac { 2} { 5} + \frac { 1} { 4} = \frac { 1} { x }`?

Answer 1

`x=20/13`

Explanation:

`2/5+1/4=1/x`

Multiply the whole equation by the lowest common denominator `5*4*x=color(red)(20x)`.

`color(red)(20x) * 2/5 +color(red)(20x) * 1/4= color(red)(20x)*1/x`

`(40x)/5 +(20x)/4=(20x)/x`

`8x+5x=20`

`13x=20`

`(13x)/13=20/13`

`x=20/13`

Another approach is to add the fractions on the left side of the equation.

`2/5+1/4=1/x`

Multiply the 1st term by `4/4` and the 2nd term by `5/5` to get a common denominator of `20`

`2/5 * 4/4 + 5/5 *1/4 = 1/xcolor(white)(aaa)`

`8/20 +5/20=1/x`

`13/20=1/xcolor(white)(aaa)`Cross multiply

`13x=20`

`(13x)/13=20/13`

`x=20/13`