Question

Question 5 of 10
Solve the rational equation:
4x/x+5 = x/x+4

Answer 1

`x = 0` or
`x = -(11)/(3)`

Explanation:

I assume the denominators are x + 5 and x + 4 although that is not what you wrote.

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

`(x + 4)(x + 5)* (4x)/(x+5) = (x + 4)(x + 5) * (x)/(x+4)`

`(x + 4)(4x) = (x + 5)(x)`

`4x^2 + 16x = x^2 + 5x`

`3x^2 + 11x = 0`

`x(3x + 11) = 0`

`x = 0` or
`3x + 11 = 0`

`x = 0` or
`3x = -11`

`x = 0` or
`x = -(11)/(3)`