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

Question

What is the solution to the equation?


`(2 )/(x) - (x)/(x + 5) = \frac{10}{ {x}^(2) + 5x }`
a. 0
b. 2
c. 0 and 2
d. no solution​

Answer 1

Hello,

answer B

2

Explanation:

`(2)/(x) -(x)/(x+5) =(10)/(x^2+5x) \\\\we\ suppose\ x\\eq 0\ and\ x\\eq -5\\\\\text{Reducing to the same denominator}\\(2(x+5)-x^2)/(x(x+5)) =(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\\`