contestada

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

Respuesta :

calculista

Answer:

x=0 is a extraneous solution

Step-by-step explanation:

we have

[tex]\frac{3}{x}=\frac{4x+3}{x^2}[/tex]

solve for x

Multiply in cross

[tex]3x^2=4x^2+3x\\4x^2-3x^2+3x=0[/tex]

x^2+3x=0

Factor x

[tex]x(x+3)=0[/tex]

The solutions are

x=0, x=-3

Remember that in the original expression the denominator cannot be equal to zero

so

x=0 is a extraneous solution

The solution is x=-3