Solve 1+2x/1+3x-1-2x/1-3x=3x-14/1-9x^2

$$\frac{ 1+2x }{ 1+3x } - \frac{ 1-2x }{ 1-3x } = \frac{ 3x-14 }{ 1-9 { x }^{ 2 } }$$

Solve for x

$$x = \frac{14}{5} = 2\frac{4}{5} = 2.8$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -\frac{1}{3},\frac{1}{3} since division by zero is not defined. Multiply both sides of the equation by \left(3x-1\right)\left(3x+1\right), the least common multiple of 1+3x,1-3x,1-9x^{2}.

$$\left(3x-1\right)\left(1+2x\right)-\left(-1-3x\right)\left(1-2x\right)=-\left(3x-14\right)$$

Use the distributive property to multiply 3x-1 by 1+2x and combine like terms.

$$x+6x^{2}-1-\left(-1-3x\right)\left(1-2x\right)=-\left(3x-14\right)$$

Use the distributive property to multiply -1-3x by 1-2x and combine like terms.

$$x+6x^{2}-1-\left(-1-x+6x^{2}\right)=-\left(3x-14\right)$$

To find the opposite of -1-x+6x^{2}, find the opposite of each term.

$$x+6x^{2}-1+1+x-6x^{2}=-\left(3x-14\right)$$

Add -1 and 1 to get 0.

$$x+6x^{2}+x-6x^{2}=-\left(3x-14\right)$$

Combine x and x to get 2x.

$$2x+6x^{2}-6x^{2}=-\left(3x-14\right)$$

Combine 6x^{2} and -6x^{2} to get 0.

$$2x=-\left(3x-14\right)$$

To find the opposite of 3x-14, find the opposite of each term.

$$2x=-3x+14$$

Add 3x to both sides.

$$2x+3x=14$$

Combine 2x and 3x to get 5x.

$$5x=14$$

Divide both sides by 5.

$$x=\frac{14}{5}$$