Solve -2ta=a-2/a+1

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

Solve for t

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

$$a\neq -1\text{ and }a\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by a+1.

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

Use the distributive property to multiply -2ta by a+1.

$$-2ta^{2}-2ta=a-2$$

Combine all terms containing t.

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

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

$$\frac{\left(-2a^{2}-2a\right)t}{-2a^{2}-2a}=\frac{a-2}{-2a^{2}-2a}$$

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

$$t=\frac{a-2}{-2a^{2}-2a}$$

Divide a-2 by -2a^{2}-2a.

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

Solve for a

$$\left\{\begin{matrix}a=-\frac{\sqrt{4t^{2}+20t+1}+2t+1}{4t}\text{; }a=-\frac{-\sqrt{4t^{2}+20t+1}+2t+1}{4t}\text{, }&t\leq -\sqrt{6}-\frac{5}{2}\text{ or }\left(t\neq 0\text{ and }t\geq \sqrt{6}-\frac{5}{2}\right)\\a=2\text{, }&t=0\end{matrix}\right.$$