Solve {l}{1/x+1+1/x^2+2x+1=0}{y=x}{z=y}{a=z}{b=a}{c=b}{text{Solvefor}dtext{where}}{d=c}

$$\left. \begin{array} { l } { \frac{1}{x + 1} + \frac{1}{x ^ {2} + 2 x + 1} = 0 }\\ { y = x }\\ { z = y }\\ { a = z }\\ { b = a }\\ { c = b }\\ { \text{Solve for } d \text{ where} } \\ { d = c } \end{array} \right.$$

Solve for x, y, z, a, b, c, d

$$d=-2$$

Solution Steps

Consider the first equation. Variable x cannot be equal to -1 since division by zero is not defined. Multiply both sides of the equation by \left(x+1\right)^{2}, the least common multiple of x+1,x^{2}+2x+1.

$$x+1+1=0$$

Add 1 and 1 to get 2.

$$x+2=0$$

Subtract 2 from both sides. Anything subtracted from zero gives its negation.

$$x=-2$$

Consider the second equation. Insert the known values of variables into the equation.

$$y=-2$$

Consider the third equation. Insert the known values of variables into the equation.

$$z=-2$$

Consider the fourth equation. Insert the known values of variables into the equation.

$$a=-2$$

Consider the fifth equation. Insert the known values of variables into the equation.

$$b=-2$$

Consider the equation (6). Insert the known values of variables into the equation.

$$c=-2$$

Consider the equation (7). Insert the known values of variables into the equation.

$$d=-2$$

The system is now solved.

$$x=-2 y=-2 z=-2 a=-2 b=-2 c=-2 d=-2$$