Solve the rational equation 4 divided by x equals quantity 3 times x plus 2 end quantity divided by x squared, and check for extraneous solutions.

x = 0; x = 2 is an extraneous solution

x = 2; x = 0 is an extraneous solution

x = 0; x = −2 is an extraneous solution

x = −2; x = 0 is an extraneous solution

Option 1- x = 0; x = 2 is an extraneous solution

Step-by-step explanation:

Given : The rational equation

To find : Solve the equation and check for extraneous solutions ?

Solution :

The equation

Cross multiply,

For extraneous solution put the value of x in the equation,

At x=0,

True

At x=2,

True

So, At x=0,2 is an extraneous solution

Therefore, Option 1 is correct.

i'm sorry mate, but i am not seeing any figures. i am unable to solve this for you.

x^2 + 81

we can factor this using difference of square binomials.

rewrite the equation:

x^2 - (-81)

factor:

(a^2 - b^2) = (√a^2 + √b^2)(√a^2 - √b^2)

(x^2 - (-81) = (x + √-81)(x - √-81)

we can remove the - from under the radical by multiplying it by i.

(x^2 - (-81) = (x + i√81)(x - i√81)

(x^2 - (-81) = (x + 9i)(x - 9i)

we can check our answer by using foil:

x^2 - 9ix + 9ix - 81i^2

x^2 - 81^2

i^2 = -1

x^2 + 81