Solve 2x-a/x-1-1/1-x=3

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

Solve for a

$$a=4-x$$

$$x\neq 1$$

Steps for Solving Linear Equation

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

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

Use the distributive property to multiply 3 by x-1.

$$2x-a+1=3x-3$$

Subtract 2x from both sides.

$$-a+1=3x-3-2x$$

Combine 3x and -2x to get x.

$$-a+1=x-3$$

Subtract 1 from both sides.

$$-a=x-3-1$$

Subtract 1 from -3 to get -4.

$$-a=x-4$$

Divide both sides by -1.

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

Dividing by -1 undoes the multiplication by -1.

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

Divide x-4 by -1.

$$a=4-x$$

Solve for x

$$x=4-a$$

$$a\neq 3$$

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.

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

Use the distributive property to multiply 3 by x-1.

$$2x-a+1=3x-3$$

Subtract 3x from both sides.

$$2x-a+1-3x=-3$$

Combine 2x and -3x to get -x.

$$-x-a+1=-3$$

Add a to both sides.

$$-x+1=-3+a$$

Subtract 1 from both sides.

$$-x=-3+a-1$$

Subtract 1 from -3 to get -4.

$$-x=-4+a$$

The equation is in standard form.

$$-x=a-4$$

Divide both sides by -1.

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

Dividing by -1 undoes the multiplication by -1.

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

Divide -4+a by -1.

$$x=4-a$$

Variable x cannot be equal to 1.

$$x=4-a\text{, }x\neq 1$$