Solve 1+2y/1+3y-1-2y/1+3y=3

$$\frac{ 1+2y }{ 1+3y } - \frac{ 1-2y }{ 1+3y } =3$$

Solve for y

$$y=-\frac{3}{5}=-0.6$$

Steps for Solving Linear Equation

Variable y cannot be equal to -\frac{1}{3} since division by zero is not defined. Multiply both sides of the equation by 3y+1.

$$1+2y-\left(1-2y\right)=3\left(3y+1\right)$$

To find the opposite of 1-2y, find the opposite of each term.

$$1+2y-1+2y=3\left(3y+1\right)$$

Subtract 1 from 1 to get 0.

$$2y+2y=3\left(3y+1\right)$$

Combine 2y and 2y to get 4y.

$$4y=3\left(3y+1\right)$$

Use the distributive property to multiply 3 by 3y+1.

$$4y=9y+3$$

Subtract 9y from both sides.

$$4y-9y=3$$

Combine 4y and -9y to get -5y.

$$-5y=3$$

Divide both sides by -5.

$$y=\frac{3}{-5}$$

Fraction \frac{3}{-5} can be rewritten as -\frac{3}{5} by extracting the negative sign.

$$y=-\frac{3}{5}$$