Question

How do you solve `\frac { 2x - 10} { x ( x + 10) } = \frac { 1} { 12}`?

Answer 1

`x =20 or x =-6`

Explanation:

In an equation which has only ONE fraction on each side, you can cross-multiply.

(This is a short cut for multiplying both sides by the LCD)

`color(red)((2x-10))/color(blue)(x(x+10)) = color(blue)(1)/color(red)(12)`

`color(blue)(1xxx(x+10)) = color(red)(12xx(2x-10)`

`x^2+10x = 24x-120" "larr` a quadratic, so make it equal to 0

`x^2 +10x-24x+120=0`

`x^2 -14x -120 =0" "larr` factorise

Find factors or `120` which differ by `14`

`120 = 20 xx6 and 20-6=14`

`(x-20)(x+6)=0`

Set each factor equal to `0`

`x-20 = 0 " "rarr x = 20`

`x+6=0" "rarr x = -6`