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

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

Solve for x

$$x=-14$$

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}.

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

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

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

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

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

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

$$x+6x^{2}-1+1+x-6x^{2}=3x+14$$

Add -1 and 1 to get 0.

$$x+6x^{2}+x-6x^{2}=3x+14$$

Combine x and x to get 2x.

$$2x+6x^{2}-6x^{2}=3x+14$$

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

$$2x=3x+14$$

Subtract 3x from both sides.

$$2x-3x=14$$

Combine 2x and -3x to get -x.

$$-x=14$$

Multiply both sides by -1.

$$x=-14$$