Question

HELP PLEASE FOR 35 POINTS!!!! 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=-3`

Explanation:

So, we are given:

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

First, we should immediately rule out 0 as an answer. This is because the if
`x=0`, the equation would be undefined.

`x\\eq 0`

Now, cross multiply.

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

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

Divide everything by x (and we can do this safely because we already know x cannot be equal to zero).

`3x=4x+3`

`-x=3`

`x=-3`

We didn't run into any possibilities for extraneous solutions.