Solve x/x-3=3--5/6-5

$$\frac { x } { x - 3 } = 3 - \frac { - 5 } { 6 - 5 }$$

Solve for x

$$x = \frac{24}{7} = 3\frac{3}{7} \approx 3.428571429$$

Steps for Solving Linear Equation

Variable x cannot be equal to 3 since division by zero is not defined. Multiply both sides of the equation by x-3.

$$x=\left(x-3\right)\times 3-\left(x-3\right)\left(-5\right)$$

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

$$x=3x-9-\left(x-3\right)\left(-5\right)$$

Use the distributive property to multiply x-3 by -5.

$$x=3x-9-\left(-5x+15\right)$$

To find the opposite of -5x+15, find the opposite of each term.

$$x=3x-9+5x-15$$

Combine 3x and 5x to get 8x.

$$x=8x-9-15$$

Subtract 15 from -9 to get -24.

$$x=8x-24$$

Subtract 8x from both sides.

$$x-8x=-24$$

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

$$-7x=-24$$

Divide both sides by -7.

$$x=\frac{-24}{-7}$$

Fraction \frac{-24}{-7} can be simplified to \frac{24}{7} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{24}{7}$$