Solve 5x+13/15-4x+5/5x-15=x/3

$$\frac{ 5x+13 }{ 15 } - \frac{ 4x+5 }{ 5x-15 } = \frac{ x }{ 3 }$$

Solve for x

$$x=54$$

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 15\left(x-3\right), the least common multiple of 15,5x-15,3.

$$\left(x-3\right)\left(5x+13\right)-3\left(4x+5\right)=\left(5x-15\right)x$$

Use the distributive property to multiply x-3 by 5x+13 and combine like terms.

$$5x^{2}-2x-39-3\left(4x+5\right)=\left(5x-15\right)x$$

Use the distributive property to multiply -3 by 4x+5.

$$5x^{2}-2x-39-12x-15=\left(5x-15\right)x$$

Combine -2x and -12x to get -14x.

$$5x^{2}-14x-39-15=\left(5x-15\right)x$$

Subtract 15 from -39 to get -54.

$$5x^{2}-14x-54=\left(5x-15\right)x$$

Use the distributive property to multiply 5x-15 by x.

$$5x^{2}-14x-54=5x^{2}-15x$$

Subtract 5x^{2} from both sides.

$$5x^{2}-14x-54-5x^{2}=-15x$$

Combine 5x^{2} and -5x^{2} to get 0.

$$-14x-54=-15x$$

Add 15x to both sides.

$$-14x-54+15x=0$$

Combine -14x and 15x to get x.

$$x-54=0$$

Add 54 to both sides. Anything plus zero gives itself.

$$x=54$$