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

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

Solve for x

$$x = \frac{55}{7} = 7\frac{6}{7} \approx 7.857142857$$

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.

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

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

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

Subtract 56 from 1 to get -55.

$$x=-55+8x$$

Subtract 8x from both sides.

$$x-8x=-55$$

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

$$-7x=-55$$

Divide both sides by -7.

$$x=\frac{-55}{-7}$$

Fraction \frac{-55}{-7} can be simplified to \frac{55}{7} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{55}{7}$$