Question

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

Answer 1

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

Explanation:

Given : The rational equation
`(4)/(x)=(3x+2)/(x^2)`

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

Solution :

The equation
`(4)/(x)=(3x+2)/(x^2)`

Cross multiply,

`4* x^2=(3x+2)* x`

`4x^2=3x^2+2x`

`4x^2-3x^2-2x=0`

`x^2-2x=0`

`x(x-2)=0`

`x=0,x-2=0`

`x=0,x=2`

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

At x=0,

`(4)/(0)=(3(0)+2)/((0)^2)`

`\infty=\infty` True

At x=2,

`(4)/(2)=(3(2)+2)/((2)^2)`

`2=(8)/(4)`

`2=2` True

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

Therefore, Option 1 is correct.