Solve 1/2^-1-1+a=1/(a^1-1)+a

$$\frac { 1 } { 2 ^ { - 1 } - 1 } + a = \frac { 1 } { ( a ^ { 1 } - 1 ) } + a$$

Solve for a

$$a=\frac{1}{2}=0.5$$

Steps for Solving Linear Equation

Variable a cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by a-1.

$$-2a+2+\left(a-1\right)a=1+\left(a-1\right)a$$

Use the distributive property to multiply a-1 by a.

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

Combine -2a and -a to get -3a.

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

Use the distributive property to multiply a-1 by a.

$$-3a+2+a^{2}=1+a^{2}-a$$

Subtract a^{2} from both sides.

$$-3a+2+a^{2}-a^{2}=1-a$$

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

$$-3a+2=1-a$$

Add a to both sides.

$$-3a+2+a=1$$

Combine -3a and a to get -2a.

$$-2a+2=1$$

Subtract 2 from both sides.

$$-2a=1-2$$

Subtract 2 from 1 to get -1.

$$-2a=-1$$

Divide both sides by -2.

$$a=\frac{-1}{-2}$$

Fraction \frac{-1}{-2} can be simplified to \frac{1}{2} by removing the negative sign from both the numerator and the denominator.

$$a=\frac{1}{2}$$