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ser-zykov [4K]
3 years ago
13

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.
Mathematics
1 answer:
denis23 [38]3 years ago
7 0

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.

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