Solve (1-x)/x-4-3(1-x)/x-3=2

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

Solve for x

$$x=5$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values 3,4 since division by zero is not defined. Multiply both sides of the equation by \left(x-4\right)\left(x-3\right), the least common multiple of x-4,x-3.

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

Use the distributive property to multiply x-3 by 1-x and combine like terms.

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

Use the distributive property to multiply x-4 by 3.

$$4x-x^{2}-3-\left(3x-12\right)\left(1-x\right)=2\left(x-4\right)\left(x-3\right)$$

Use the distributive property to multiply 3x-12 by 1-x and combine like terms.

$$4x-x^{2}-3-\left(15x-3x^{2}-12\right)=2\left(x-4\right)\left(x-3\right)$$

To find the opposite of 15x-3x^{2}-12, find the opposite of each term.

$$4x-x^{2}-3-15x+3x^{2}+12=2\left(x-4\right)\left(x-3\right)$$

Combine 4x and -15x to get -11x.

$$-11x-x^{2}-3+3x^{2}+12=2\left(x-4\right)\left(x-3\right)$$

Combine -x^{2} and 3x^{2} to get 2x^{2}.

$$-11x+2x^{2}-3+12=2\left(x-4\right)\left(x-3\right)$$

Add -3 and 12 to get 9.

$$-11x+2x^{2}+9=2\left(x-4\right)\left(x-3\right)$$

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

$$-11x+2x^{2}+9=\left(2x-8\right)\left(x-3\right)$$

Use the distributive property to multiply 2x-8 by x-3 and combine like terms.

$$-11x+2x^{2}+9=2x^{2}-14x+24$$

Subtract 2x^{2} from both sides.

$$-11x+2x^{2}+9-2x^{2}=-14x+24$$

Combine 2x^{2} and -2x^{2} to get 0.

$$-11x+9=-14x+24$$

Add 14x to both sides.

$$-11x+9+14x=24$$

Combine -11x and 14x to get 3x.

$$3x+9=24$$

Subtract 9 from both sides.

$$3x=24-9$$

Subtract 9 from 24 to get 15.

$$3x=15$$

Divide both sides by 3.

$$x=\frac{15}{3}$$

Divide 15 by 3 to get 5.

$$x=5$$