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Find all values of x such that

\( 9 + \frac{27}{x} + \frac{8}{x^2} = 0\)
If you find more than one value, then list your solutions, separated by commas.

 Aug 16, 2020
edited by Creampuff  Aug 16, 2020
 #1
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+1

Solve for x:
9 + 27/x + 8/x^2 = 0

Bring 9 + 27/x + 8/x^2 together using the common denominator x^2:

(9 x^2 + 27 x + 8)/x^2 = 0

Multiply both sides by x^2:
9 x^2 + 27 x + 8 = 0

The left hand side factors into a product with two terms:
(3 x + 1) (3 x + 8) = 0

Split into two equations:
3 x + 1 = 0 or 3 x + 8 = 0

Subtract 1 from both sides:
3 x = -1 or 3 x + 8 = 0

Divide both sides by 3:
x = -1/3 or 3 x + 8 = 0

Subtract 8 from both sides:
x = -1/3 or 3 x = -8

Divide both sides by 3:

 x = -1/3              or               x = -8/3

 Aug 16, 2020
 #2
avatar+110762 
+2

You can see straight off that x cannot be 0.

So

I would start by multiplying both sides by x^2

 

That will get rid of all the fractions and you will be left with just a quadratic to solve.

 

this is much the same as what guest has done.

 Aug 17, 2020

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