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

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

Solve for a

$$a=6-3x$$

$$x\neq 1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x-1, the least common multiple of x-1,1-x.

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

Use the distributive property to multiply 4 by x-1.

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

Subtract x from both sides.

$$2-a=4x-4-x$$

Combine 4x and -x to get 3x.

$$2-a=3x-4$$

Subtract 2 from both sides.

$$-a=3x-4-2$$

Subtract 2 from -4 to get -6.

$$-a=3x-6$$

Divide both sides by -1.

$$\frac{-a}{-1}=\frac{3x-6}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$a=\frac{3x-6}{-1}$$

Divide -6+3x by -1.

$$a=6-3x$$

Solve for x

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

$$a\neq 3$$

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 x-1, the least common multiple of x-1,1-x.

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

Use the distributive property to multiply 4 by x-1.

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

Subtract 4x from both sides.

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

Combine x and -4x to get -3x.

$$-3x+2-a=-4$$

Subtract 2 from both sides.

$$-3x-a=-4-2$$

Subtract 2 from -4 to get -6.

$$-3x-a=-6$$

Add a to both sides.

$$-3x=-6+a$$

The equation is in standard form.

$$-3x=a-6$$

Divide both sides by -3.

$$\frac{-3x}{-3}=\frac{a-6}{-3}$$

Dividing by -3 undoes the multiplication by -3.

$$x=\frac{a-6}{-3}$$

Divide -6+a by -3.

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

Variable x cannot be equal to 1.

$$x=-\frac{a}{3}+2\text{, }x\neq 1$$