SOLUTION: 5/3x + 2/x^2 = 7/9 find and name the domain then solve

Question 389452: 5/3x + 2/x^2 = 7/9
find and name the domain then solve
Answer by haileytucki(390) (Show Source): You can put this solution on YOUR website!
(5)/(3x)+(2)/(x^(2))=(7)/(9)
Find the LCD (least common denominator) of (5)/(3x)+(2)/(x^(2))+(7)/(9).
Least common denominator: 9x^(2)
Multiply each term in the equation by 9x^(2) in order to remove all the denominators from the equation.
(5)/(3x)*9x^(2)+(2)/(x^(2))*9x^(2)=(7)/(9)*9x^(2)
Simplify the left-hand side of the equation by canceling the common factors.
15x+18=(7)/(9)*9x^(2)
Simplify the right-hand side of the equation by simplifying each term.
15x+18=7x^(2)
Since 7x^(2) contains the variable to solve for, move it to the left-hand side of the equation by subtracting 7x^(2) from both sides.
15x+18-7x^(2)=0
Move all terms not containing x to the right-hand side of the equation.
-7x^(2)+15x+18=0
Multiply each term in the equation by -1.
7x^(2)-15x-18=0
In this problem (6)/(7)*-3=-18 and (6)/(7)-3=-15, so insert (6)/(7) as the right hand term of one factor and -3 as the right-hand term of the other factor.
(x+(6)/(7))(x-3)=0
Remove the fraction by multiplying the first term of the factor by the denominator of the second term.
(7x+6)(x-3)=0
Set each of the factors of the left-hand side of the equation equal to 0.
7x+6=0_x-3=0
Since 6 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 6 from both sides.
7x=-6_x-3=0
Divide each term in the equation by 7.
(7x)/(7)=-(6)/(7)_x-3=0
Simplify the left-hand side of the equation by canceling the common factors.
x=-(6)/(7)_x-3=0
Set each of the factors of the left-hand side of the equation equal to 0.
x=-(6)/(7)_x-3=0
Since -3 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 3 to both sides.
x=-(6)/(7)_x=3
The complete solution is the set of the individual solutions.
x=-(6)/(7),3
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