Answer:
Option 1- x = 0; x = 2 is an extraneous solution
Step-by-step explanation:
Given : The rational equation [tex]\frac{4}{x}=\frac{3x+2}{x^2}[/tex]
To find : Solve the equation and check for extraneous solutions ?
Solution :
The equation [tex]\frac{4}{x}=\frac{3x+2}{x^2}[/tex]
Cross multiply,
[tex]4\times x^2=(3x+2)\times x[/tex]
[tex]4x^2=3x^2+2x[/tex]
[tex]4x^2-3x^2-2x=0[/tex]
[tex]x^2-2x=0[/tex]
[tex]x(x-2)=0[/tex]
[tex]x=0,x-2=0[/tex]
[tex]x=0,x=2[/tex]
For extraneous solution put the value of x in the equation,
At x=0,
[tex]\frac{4}{0}=\frac{3(0)+2}{(0)^2}[/tex]
[tex]\infty=\infty[/tex] True
At x=2,
[tex]\frac{4}{2}=\frac{3(2)+2}{(2)^2}[/tex]
[tex]2=\frac{8}{4}[/tex]
[tex]2=2[/tex] True
So, At x=0,2 is an extraneous solution
Therefore, Option 1 is correct.
