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

Answer:

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

Step-by-step explanation:

Given : The rational equation $\frac{4}{x}=\frac{3x+2}{x^2}$

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

Solution :

The equation $\frac{4}{x}=\frac{3x+2}{x^2}$

Cross multiply,

$4\times x^2=(3x+2)\times x$

$4x^2=3x^2+2x$

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

$x^2-2x=0$

$x(x-2)=0$

$x=0,x-2=0$

$x=0,x=2$

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

At x=0,

$\frac{4}{0}=\frac{3(0)+2}{(0)^2}$

$\infty=\infty$ True

At x=2,

$\frac{4}{2}=\frac{3(2)+2}{(2)^2}$

$2=\frac{8}{4}$

$2=2$ True

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

Therefore, Option 1 is correct.