Question

Please explain how you worked the problem to find x!


1/x +1/(x+4) =1/5

Answer 1

`(1)/(x) +(1)/(x+4)` (by taking the common factor for the two elements of the equation

now we can add both of the equation as the denominators have the same value.

`(x+4+x)/(x*(x+4))=(2x+4)/(x^(2)+4x) = (1)/(5)` by multiplying both sides by
`5*(x^(2)+4x)`

`5*(2x+4)=x^(2) +4x`

`10x+20=x^(2)+4x` by subtracting both sides by (10x+20)

`x^(2) -6x -20 = 0` (by using the quadratic formula)
we will find two answers for this equation
x={
`(-6- √(116))/(-2)` and
`(-6+√(116))/(-2)`