Solve 6u^-1/2-13u^-1/4+6=0

$$6 u ^ { - 1 } / 2 - 13 u ^ { - 1 } / 4 + 6 = 0$$

Solve for u

$$u=\frac{1}{24}\approx 0.041666667$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 4, the least common multiple of 2,4.

$$2\times 6u^{-1}-13u^{-1}+24=0$$

Multiply 2 and 6 to get 12.

$$12u^{-1}-13u^{-1}+24=0$$

Combine 12u^{-1} and -13u^{-1} to get -u^{-1}.

$$-u^{-1}+24=0$$

Subtract 24 from both sides. Anything subtracted from zero gives its negation.

$$-u^{-1}=-24$$

Divide both sides by -1.

$$u^{-1}=\frac{-24}{-1}$$

Fraction \frac{-24}{-1} can be simplified to 24 by removing the negative sign from both the numerator and the denominator.

$$u^{-1}=24$$

Reorder the terms.

$$\frac{1}{u}=24$$

Variable u cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by u.

$$1=24u$$

Swap sides so that all variable terms are on the left hand side.

$$24u=1$$

Divide both sides by 24.

$$u=\frac{1}{24}$$