Question

How do you solve `1/(4 -x) = x/8`?

Answer 1

Below

Explanation:

`1/(4-x)=x/8`

`1/(4-x)times8/8 = x/8times(4-x)/(4-x)`

`8/(8(4-x)) = (x(4-x))/(8(4-x))`

`8 = x(4-x)`

`8 = 4x-x^2`

`x^2-4x+8=0`

Using the quadratic formula:

`x = (-b+-sqrt(b^2-4ac))/(2a)`

`x = (4+-sqrt(16-4times1times8))/(2times1)`

`x = (4+-sqrt(-16))/2`

If you haven't learnt complex numbers yet, then you can ignore the following lines and just state that since the discriminant is less than 0, then there is no solution to the equation.

`x = (4+-sqrt(16times-1))/2`

`x = (4+-4i)/2`

`x = 2+-2i`

`x^2-4x+8=0`

`(x-(2-2i))(x-(2+2i))=0`

`(x-2+2i)(x-2-2i)=0`