Solve 2a^2+a-1/ax=a+1

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

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{a}{2a-1}\text{, }&a\neq \frac{1}{2}\text{ and }a\neq 0\\x\in \mathrm{C}\text{, }&a=-1\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by a.

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

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

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

Divide both sides by 2a^{2}+a-1.

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

Dividing by 2a^{2}+a-1 undoes the multiplication by 2a^{2}+a-1.

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

Divide a\left(1+a\right) by 2a^{2}+a-1.

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

Solve for x

$$\left\{\begin{matrix}x=\frac{a}{2a-1}\text{, }&a\neq \frac{1}{2}\text{ and }a\neq 0\\x\in \mathrm{R}\text{, }&a=-1\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by a.

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

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

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

Divide both sides by 2a^{2}+a-1.

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

Dividing by 2a^{2}+a-1 undoes the multiplication by 2a^{2}+a-1.

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

Divide a\left(1+a\right) by 2a^{2}+a-1.

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

Solve for a

$$\left\{\begin{matrix}\\a=-1\text{, }&\text{unconditionally}\\a=\frac{x}{2x-1}\text{, }&x\neq 0\text{ and }x\neq \frac{1}{2}\end{matrix}\right.$$