Solve x+6/x-9=5

$$\frac { x + 6 } { x - 9 } = 5$$

Solve for x

$$x = \frac{51}{4} = 12\frac{3}{4} = 12.75$$

Steps for Solving Linear Equation

Variable x cannot be equal to 9 since division by zero is not defined. Multiply both sides of the equation by x-9.

$$x+6=5\left(x-9\right)$$

Use the distributive property to multiply 5 by x-9.

$$x+6=5x-45$$

Subtract 5x from both sides.

$$x+6-5x=-45$$

Combine x and -5x to get -4x.

$$-4x+6=-45$$

Subtract 6 from both sides.

$$-4x=-45-6$$

Subtract 6 from -45 to get -51.

$$-4x=-51$$

Divide both sides by -4.

$$x=\frac{-51}{-4}$$

Fraction \frac{-51}{-4} can be simplified to \frac{51}{4} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{51}{4}$$