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

Answer:

$x=-3$

Step-by-step explanation:

So, we are given:

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

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

$x\neq 0$

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.