Solve x+2*3a+1/a+1--2/1+a=4

$$x + 2 \cdot \frac { 3 a + 1 } { a + 1 } - \frac { - 2 } { 1 + a } = 4$$

Solve for a

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

$$x\neq -2$$

Steps for Solving Linear Equation

Variable a cannot be equal to -1 since division by zero is not defined. Multiply both sides of the equation by a+1.

$$\left(a+1\right)x+2\left(3a+1\right)+2=4\left(a+1\right)$$

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

$$ax+x+2\left(3a+1\right)+2=4\left(a+1\right)$$

Use the distributive property to multiply 2 by 3a+1.

$$ax+x+6a+2+2=4\left(a+1\right)$$

Add 2 and 2 to get 4.

$$ax+x+6a+4=4\left(a+1\right)$$

Use the distributive property to multiply 4 by a+1.

$$ax+x+6a+4=4a+4$$

Subtract 4a from both sides.

$$ax+x+6a+4-4a=4$$

Combine 6a and -4a to get 2a.

$$ax+x+2a+4=4$$

Subtract x from both sides.

$$ax+2a+4=4-x$$

Subtract 4 from both sides.

$$ax+2a=4-x-4$$

Subtract 4 from 4 to get 0.

$$ax+2a=-x$$

Combine all terms containing a.

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

Divide both sides by x+2.

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

Dividing by x+2 undoes the multiplication by x+2.

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

Variable a cannot be equal to -1.

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

Solve for x

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

$$a\neq -1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by a+1.

$$\left(a+1\right)x+2\left(3a+1\right)+2=4\left(a+1\right)$$

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

$$ax+x+2\left(3a+1\right)+2=4\left(a+1\right)$$

Use the distributive property to multiply 2 by 3a+1.

$$ax+x+6a+2+2=4\left(a+1\right)$$

Add 2 and 2 to get 4.

$$ax+x+6a+4=4\left(a+1\right)$$

Use the distributive property to multiply 4 by a+1.

$$ax+x+6a+4=4a+4$$

Subtract 6a from both sides.

$$ax+x+4=4a+4-6a$$

Combine 4a and -6a to get -2a.

$$ax+x+4=-2a+4$$

Subtract 4 from both sides.

$$ax+x=-2a+4-4$$

Subtract 4 from 4 to get 0.

$$ax+x=-2a$$

Combine all terms containing x.

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

Divide both sides by a+1.

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

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

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