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BaLLatris [955]
2 years ago
12

Which of the following statements are true about the given rational equation? check all of the boxes that apply. 4 x 6 1 x2 = x

10 x3 6x2 x = 1 is a solution. x = 0 is a solution. x = –1 is a solution. x = –6 is a solution.
Mathematics
1 answer:
Agata [3.3K]2 years ago
3 0

We can actually see that the statements that are true are:

A. x = 1 is a solution.

C. x = –1 is a solution.

<h3>What is rational equation?</h3>

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:

\frac{4}{x + 6}  +  \frac{1}{ {x}^{2} }  =  \frac{x + 10}{ {x}^{3} + 6 {x}^{2}  }

It's clear that: x ≠ 0 and x ≠ -6.

Looking for the LCM of the left hand side, we will have:

\frac{4}{x + 6}  +  \frac{1}{ {x}^{2} }  =  \frac{4 {x}^{2 }  + (x + 6)}{(x + 6) {x}^{2} }

So, we will see that left hand side and right hand side are equal.

4 {x}^{2}  + x + 6 = x + 10

4 {x}^{2}  = 10 - 6

4 {x}^{2}  = 4

{x}^{2}  = 1

x = 1

or

x =  - 1

So, we can see that options A and C are correct.

Learn more about rational equation on brainly.com/question/11611235

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