Solve -1/7=x+1/1-x

$$\frac { - 1 } { 7 } = \frac { x + 1 } { 1 - x }$$

Solve for x

$$x = -\frac{4}{3} = -1\frac{1}{3} \approx -1.333333333$$

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 7\left(x-1\right), the least common multiple of 7,1-x.

$$\left(x-1\right)\left(-1\right)=-7\left(x+1\right)$$

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

$$-x+1=-7\left(x+1\right)$$

Use the distributive property to multiply -7 by x+1.

$$-x+1=-7x-7$$

Add 7x to both sides.

$$-x+1+7x=-7$$

Combine -x and 7x to get 6x.

$$6x+1=-7$$

Subtract 1 from both sides.

$$6x=-7-1$$

Subtract 1 from -7 to get -8.

$$6x=-8$$

Divide both sides by 6.

$$x=\frac{-8}{6}$$

Reduce the fraction \frac{-8}{6} to lowest terms by extracting and canceling out 2.

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