Solve the rational equation x over 5 equals x squared over quantity x plus 2 and check for extraneous solutions.

x = 0; x equals negative one half is an extraneous solution

x equals one half; x = 0 is an extraneous solution

x = 0 and x equals one half

x = 0 and x equals negative one half

c

Step-by-step explanation:

x=0 and x = one half (1/2) is the solution of rational equation:

Option C is correct.

Step-by-step explanation:

We need to solve rational equation: and identify extraneous solutions.

Solving:

Cross multiplying and solving:

So, values of x are x = 0 and x=1/2

Checking for extraneous solutions.

To check for extraneous solutions we will put value of x in the given rational equation and check if it satisfies the equation or not.

Putting x=0

Putting x = 1/2

Since both values satisfies the given equation so, there is no extraneous solutions.

x=0 and x = one half (1/2) is the solution of rational equation:

Option C is correct.