Solve 5x+13/5x+4-4-6x/3x-1=3

$$\frac{ 5x+13 }{ 5x+4 } - \frac{ 4-6x }{ 3x-1 } = 3$$

Solve for x

$$x=1$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -\frac{4}{5},\frac{1}{3} since division by zero is not defined. Multiply both sides of the equation by \left(3x-1\right)\left(5x+4\right), the least common multiple of 5x+4,3x-1.

$$\left(3x-1\right)\left(5x+13\right)-\left(5x+4\right)\left(4-6x\right)=3\left(3x-1\right)\left(5x+4\right)$$

Use the distributive property to multiply 3x-1 by 5x+13 and combine like terms.

$$15x^{2}+34x-13-\left(5x+4\right)\left(4-6x\right)=3\left(3x-1\right)\left(5x+4\right)$$

Use the distributive property to multiply 5x+4 by 4-6x and combine like terms.

$$15x^{2}+34x-13-\left(-4x-30x^{2}+16\right)=3\left(3x-1\right)\left(5x+4\right)$$

To find the opposite of -4x-30x^{2}+16, find the opposite of each term.

$$15x^{2}+34x-13+4x+30x^{2}-16=3\left(3x-1\right)\left(5x+4\right)$$

Combine 34x and 4x to get 38x.

$$15x^{2}+38x-13+30x^{2}-16=3\left(3x-1\right)\left(5x+4\right)$$

Combine 15x^{2} and 30x^{2} to get 45x^{2}.

$$45x^{2}+38x-13-16=3\left(3x-1\right)\left(5x+4\right)$$

Subtract 16 from -13 to get -29.

$$45x^{2}+38x-29=3\left(3x-1\right)\left(5x+4\right)$$

Use the distributive property to multiply 3 by 3x-1.

$$45x^{2}+38x-29=\left(9x-3\right)\left(5x+4\right)$$

Use the distributive property to multiply 9x-3 by 5x+4 and combine like terms.

$$45x^{2}+38x-29=45x^{2}+21x-12$$

Subtract 45x^{2} from both sides.

$$45x^{2}+38x-29-45x^{2}=21x-12$$

Combine 45x^{2} and -45x^{2} to get 0.

$$38x-29=21x-12$$

Subtract 21x from both sides.

$$38x-29-21x=-12$$

Combine 38x and -21x to get 17x.

$$17x-29=-12$$

Add 29 to both sides.

$$17x=-12+29$$

Add -12 and 29 to get 17.

$$17x=17$$

Divide both sides by 17.

$$x=\frac{17}{17}$$

Divide 17 by 17 to get 1.

$$x=1$$