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

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

Solve for x

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

Steps for Solving Linear Equation

Variable x cannot be equal to -2 since division by zero is not defined. Multiply both sides of the equation by a\left(x+2\right), the least common multiple of x+2,a.

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

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

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

Use the distributive property to multiply a by x+2.

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

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

$$a^{2}+a-ax-2a=x+2$$

Combine a and -2a to get -a.

$$a^{2}-a-ax=x+2$$

Subtract x from both sides.

$$a^{2}-a-ax-x=2$$

Subtract a^{2} from both sides.

$$-a-ax-x=2-a^{2}$$

Add a to both sides.

$$-ax-x=2-a^{2}+a$$

Combine all terms containing x.

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

The equation is in standard form.

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

Divide both sides by -a-1.

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

Dividing by -a-1 undoes the multiplication by -a-1.

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

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

$$x=a-2$$

Variable x cannot be equal to -2.

$$x=a-2\text{, }x\neq -2$$

Solve for a

$$a=x+2$$

$$a=-1\text{, }x\neq -2$$