Solve 1/41/x-1-2=3/1-x

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

Solve for x

$$x = \frac{21}{8} = 2\frac{5}{8} = 2.625$$

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), the least common multiple of 4,x-1,1-x.

$$\frac{1}{4}\times 4\times 1+4\left(x-1\right)\left(-2\right)=-4\times 3$$

Multiply \frac{1}{4} and 4 to get 1.

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

Multiply 4 and -2 to get -8.

$$1-8\left(x-1\right)=-4\times 3$$

Use the distributive property to multiply -8 by x-1.

$$1-8x+8=-4\times 3$$

Add 1 and 8 to get 9.

$$9-8x=-4\times 3$$

Multiply -4 and 3 to get -12.

$$9-8x=-12$$

Subtract 9 from both sides.

$$-8x=-12-9$$

Subtract 9 from -12 to get -21.

$$-8x=-21$$

Divide both sides by -8.

$$x=\frac{-21}{-8}$$

Fraction \frac{-21}{-8} can be simplified to \frac{21}{8} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{21}{8}$$