Solve 2x/x-7=3+1-x/x-5

$$\frac { 2 x } { x - 7 } = 3 + \frac { 1 - x } { x - 5 }$$

Solve for x

$$x = \frac{49}{9} = 5\frac{4}{9} \approx 5.444444444$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values 5,7 since division by zero is not defined. Multiply both sides of the equation by \left(x-7\right)\left(x-5\right), the least common multiple of x-7,x-5.

$$\left(x-5\right)\times 2x=\left(x-7\right)\left(x-5\right)\times 3+\left(x-7\right)\left(1-x\right)$$

Use the distributive property to multiply x-5 by 2.

$$\left(2x-10\right)x=\left(x-7\right)\left(x-5\right)\times 3+\left(x-7\right)\left(1-x\right)$$

Use the distributive property to multiply 2x-10 by x.

$$2x^{2}-10x=\left(x-7\right)\left(x-5\right)\times 3+\left(x-7\right)\left(1-x\right)$$

Use the distributive property to multiply x-7 by x-5 and combine like terms.

$$2x^{2}-10x=\left(x^{2}-12x+35\right)\times 3+\left(x-7\right)\left(1-x\right)$$

Use the distributive property to multiply x^{2}-12x+35 by 3.

$$2x^{2}-10x=3x^{2}-36x+105+\left(x-7\right)\left(1-x\right)$$

Use the distributive property to multiply x-7 by 1-x and combine like terms.

$$2x^{2}-10x=3x^{2}-36x+105+8x-x^{2}-7$$

Combine -36x and 8x to get -28x.

$$2x^{2}-10x=3x^{2}-28x+105-x^{2}-7$$

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

$$2x^{2}-10x=2x^{2}-28x+105-7$$

Subtract 7 from 105 to get 98.

$$2x^{2}-10x=2x^{2}-28x+98$$

Subtract 2x^{2} from both sides.

$$2x^{2}-10x-2x^{2}=-28x+98$$

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

$$-10x=-28x+98$$

Add 28x to both sides.

$$-10x+28x=98$$

Combine -10x and 28x to get 18x.

$$18x=98$$

Divide both sides by 18.

$$x=\frac{98}{18}$$

Reduce the fraction \frac{98}{18} to lowest terms by extracting and canceling out 2.

$$x=\frac{49}{9}$$