Question

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

Answer 1

x=0 is a extraneous solution

Explanation:

we have

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

solve for x

Multiply in cross

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

x^2+3x=0

Factor x

`x(x+3)=0`

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