what is the solution to the equation?
[tex] \frac{2 }{x} - \frac{x}{x + 5} = \frac{10}{ {x}^{2} + 5x } [/tex]
a. 0
b. 2
c. 0 and 2
d. no solution​

Respuesta :

caylus

Answer:

Hello,

answer B

2

Step-by-step explanation:

[tex]\dfrac{2}{x} -\dfrac{x}{x+5} =\dfrac{10}{x^2+5x} \\\\we\ suppose\ x\neq 0\ and\ x\neq -5\\\\\text{Reducing to the same denominator}\\\dfrac{2(x+5)-x^2}{x(x+5)} =\dfrac{10}{x^2+5x} \\\\Simplify\ by\ x^2+5x\\\\2x+10-x^2=10\\\\-x^2+2x=0\\\\-x(x-2)=0\\\\roots\ are\ 2 \ and\ 0\ (to\ be\ excluded)\\\\Root=2\\[/tex]