We can actually see that the statements that are true are:
A. x = 1 is a solution.
C. x = –1 is a solution.
What is rational equation?
Rational equation is actually known as an equation that contains at least one fraction. The denominator and numerator are known to be polynomials.
We can see then that:
[tex] \frac{4}{x + 6} + \frac{1}{ {x}^{2} } = \frac{x + 10}{ {x}^{3} + 6 {x}^{2} } [/tex]
It's clear that: x ≠ 0 and x ≠ -6.
Looking for the LCM of the left hand side, we will have:
[tex] \frac{4}{x + 6} + \frac{1}{ {x}^{2} } = \frac{4 {x}^{2 } + (x + 6)}{(x + 6) {x}^{2} } [/tex]
So, we will see that left hand side and right hand side are equal.
[tex]4 {x}^{2} + x + 6 = x + 10[/tex]
[tex]4 {x}^{2} = 10 - 6[/tex]
[tex]4 {x}^{2} = 4[/tex]
[tex] {x}^{2} = 1[/tex]
[tex] x = 1[/tex]
or
[tex]x = - 1[/tex]
So, we can see that options A and C are correct.
Learn more about rational equation on https://brainly.com/question/11611235
