Question

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

Answer 1

Answer:

$x = 0$  or  $x = -\dfrac{11}{3}$

Step-by-step explanation:

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

$\dfrac{4x}{x+5} = \dfrac{x}{x+4}$

$(x + 4)(x + 5)\times \dfrac{4x}{x+5} = (x + 4)(x + 5) \times \dfrac{x}{x+4}$

$(x + 4)(4x) = (x + 5)(x)$

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

$3x^2 + 11x = 0$

$x(3x + 11) = 0$

$x = 0$  or  $3x + 11 = 0$

$x = 0$  or  $3x = -11$

$x = 0$  or  $x = -\dfrac{11}{3}$