Solve for x
x=-\frac{1}{15}\approx -0.066666667
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Linear Equation
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\frac { 9 } { 6 x ^ { 2 } + x - 2 } = \frac { 5 } { 2 x - 1 }
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9=\left(3x+2\right)\times 5
Variable x cannot be equal to any of the values -\frac{2}{3},\frac{1}{2} since division by zero is not defined. Multiply both sides of the equation by \left(2x-1\right)\left(3x+2\right), the least common multiple of 6x^{2}+x-2,2x-1.
9=15x+10
Use the distributive property to multiply 3x+2 by 5.
15x+10=9
Swap sides so that all variable terms are on the left hand side.
15x=9-10
Subtract 10 from both sides.
15x=-1
Subtract 10 from 9 to get -1.
x=\frac{-1}{15}
Divide both sides by 15.
x=-\frac{1}{15}
Fraction \frac{-1}{15} can be rewritten as -\frac{1}{15} by extracting the negative sign.
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