Solve x/x-7=1/7-x+8

$$\frac { x } { x - 7 } = \frac { 1 } { 7 - x } + 8$$

Solve for x

$$x = \frac{57}{7} = 8\frac{1}{7} \approx 8.142857143$$

Steps for Solving Linear Equation

Variable x cannot be equal to 7 since division by zero is not defined. Multiply both sides of the equation by x-7, the least common multiple of x-7,7-x.

$$x=-1+\left(x-7\right)\times 8$$

Use the distributive property to multiply x-7 by 8.

$$x=-1+8x-56$$

Subtract 56 from -1 to get -57.

$$x=-57+8x$$

Subtract 8x from both sides.

$$x-8x=-57$$

Combine x and -8x to get -7x.

$$-7x=-57$$

Divide both sides by -7.

$$x=\frac{-57}{-7}$$

Fraction \frac{-57}{-7} can be simplified to \frac{57}{7} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{57}{7}$$