Solve 1-a^2/a+a-3=11

$$\frac { 1 - a ^ { 2 } } { a } + a - 3 = 11$$

Solve for a

$$a=\frac{1}{14}\approx 0.071428571$$

Steps for Solving Linear Equation

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

$$1-a^{2}+aa+a\left(-3\right)=11a$$

Multiply a and a to get a^{2}.

$$1-a^{2}+a^{2}+a\left(-3\right)=11a$$

Combine -a^{2} and a^{2} to get 0.

$$1+a\left(-3\right)=11a$$

Subtract 11a from both sides.

$$1+a\left(-3\right)-11a=0$$

Combine a\left(-3\right) and -11a to get -14a.

$$1-14a=0$$

Subtract 1 from both sides. Anything subtracted from zero gives its negation.

$$-14a=-1$$

Divide both sides by -14.

$$a=\frac{-1}{-14}$$

Fraction \frac{-1}{-14} can be simplified to \frac{1}{14} by removing the negative sign from both the numerator and the denominator.

$$a=\frac{1}{14}$$