Solve 2/x+1-2/4x+4=1/(x+1)^2

$$\frac { 2 } { x + 1 } - \frac { 2 } { 4 x + 4 } = \frac { 1 } { ( x + 1 ) ^ { 2 } }$$

Solve for x

$$x=-\frac{1}{3}\approx -0.333333333$$

Steps for Solving Linear Equation

Variable x cannot be equal to -1 since division by zero is not defined. Multiply both sides of the equation by 4\left(x+1\right)^{2}, the least common multiple of x+1,4x+4,\left(x+1\right)^{2}.

$$\left(4x+4\right)\times 2-\left(x+1\right)\times 2=4$$

Use the distributive property to multiply 4x+4 by 2.

$$8x+8-\left(x+1\right)\times 2=4$$

Use the distributive property to multiply x+1 by 2.

$$8x+8-\left(2x+2\right)=4$$

To find the opposite of 2x+2, find the opposite of each term.

$$8x+8-2x-2=4$$

Combine 8x and -2x to get 6x.

$$6x+8-2=4$$

Subtract 2 from 8 to get 6.

$$6x+6=4$$

Subtract 6 from both sides.

$$6x=4-6$$

Subtract 6 from 4 to get -2.

$$6x=-2$$

Divide both sides by 6.

$$x=\frac{-2}{6}$$

Reduce the fraction \frac{-2}{6} to lowest terms by extracting and canceling out 2.

$$x=-\frac{1}{3}$$