Solve 3-1/x-9/x^2=0

Evaluate

3 - \frac{1}{x} - \frac{9}{x ^{2}} = 0

Find the domain

More Steps

3 - \frac{1}{x} - \frac{9}{x ^{2}} = 0, x \neq = 0

Multiply both sides of the equation by LCD

(3 - \frac{1}{x} - \frac{9}{x ^{2}}) x^{2} = 0 \times x^{2}

Simplify the equation

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3 x^{2} - x - 9 = 0 \times x^{2}

Any expression multiplied by 0 equals 0

3 x^{2} - x - 9 = 0

Substitute a= 3,b= - 1 and c= - 9 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{1 \pm ( - 1 ) ^{2} - 4 \times 3 ( - 9 )}{2 \times 3}

Simplify the expression

x = \frac{1 \pm ( - 1 ) ^{2} - 4 \times 3 ( - 9 )}{6}

Simplify the expression

More Steps

x = \frac{1 \pm 109}{6}

Separate the equation into 2 possible cases

x = \frac{1 + 109}{6} x = \frac{1 - 109}{6}

Check if the solution is in the defined range

x = \frac{1 + 109}{6} x = \frac{1 - 109}{6}, x \neq = 0

Find the intersection of the solution and the defined range

x = \frac{1 + 109}{6} x = \frac{1 - 109}{6}

Solution

x_{1} = \frac{1 - 109}{6}, x_{2} = \frac{1 + 109}{6}

Alternative Form

x_{1} \approx - 1.573384, x_{2} \approx 1.906718

3 1/x 9/x^2=0