Solve 2x+3/5x-1=6x+4/15x+2

$$\frac { 2 x + 3 } { 5 x - 1 } = \frac { 6 x + 4 } { 15 x + 2 }$$

Solve for x

$$x=-\frac{2}{7}\approx -0.285714286$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -\frac{2}{15},\frac{1}{5} since division by zero is not defined. Multiply both sides of the equation by \left(5x-1\right)\left(15x+2\right), the least common multiple of 5x-1,15x+2.

$$\left(15x+2\right)\left(2x+3\right)=\left(5x-1\right)\left(6x+4\right)$$

Use the distributive property to multiply 15x+2 by 2x+3 and combine like terms.

$$30x^{2}+49x+6=\left(5x-1\right)\left(6x+4\right)$$

Use the distributive property to multiply 5x-1 by 6x+4 and combine like terms.

$$30x^{2}+49x+6=30x^{2}+14x-4$$

Subtract 30x^{2} from both sides.

$$30x^{2}+49x+6-30x^{2}=14x-4$$

Combine 30x^{2} and -30x^{2} to get 0.

$$49x+6=14x-4$$

Subtract 14x from both sides.

$$49x+6-14x=-4$$

Combine 49x and -14x to get 35x.

$$35x+6=-4$$

Subtract 6 from both sides.

$$35x=-4-6$$

Subtract 6 from -4 to get -10.

$$35x=-10$$

Divide both sides by 35.

$$x=\frac{-10}{35}$$

Reduce the fraction \frac{-10}{35} to lowest terms by extracting and canceling out 5.

$$x=-\frac{2}{7}$$