Solve 3x+1/6x-2=2x+5/4x-13

$$\frac{ 3x+1 }{ 6x-2 } = \frac{ 2x+5 }{ 4x-13 }$$

Solve for x

$$x=-\frac{3}{61}\approx -0.049180328$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values \frac{1}{3},\frac{13}{4} since division by zero is not defined. Multiply both sides of the equation by 2\left(3x-1\right)\left(4x-13\right), the least common multiple of 6x-2,4x-13.

$$\left(4x-13\right)\left(3x+1\right)=\left(6x-2\right)\left(2x+5\right)$$

Use the distributive property to multiply 4x-13 by 3x+1 and combine like terms.

$$12x^{2}-35x-13=\left(6x-2\right)\left(2x+5\right)$$

Use the distributive property to multiply 6x-2 by 2x+5 and combine like terms.

$$12x^{2}-35x-13=12x^{2}+26x-10$$

Subtract 12x^{2} from both sides.

$$12x^{2}-35x-13-12x^{2}=26x-10$$

Combine 12x^{2} and -12x^{2} to get 0.

$$-35x-13=26x-10$$

Subtract 26x from both sides.

$$-35x-13-26x=-10$$

Combine -35x and -26x to get -61x.

$$-61x-13=-10$$

Add 13 to both sides.

$$-61x=-10+13$$

Add -10 and 13 to get 3.

$$-61x=3$$

Divide both sides by -61.

$$x=\frac{3}{-61}$$

Fraction \frac{3}{-61} can be rewritten as -\frac{3}{61} by extracting the negative sign.

$$x=-\frac{3}{61}$$