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

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

Solve for m

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

Steps for Solving Linear Equation

Variable m 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(3m-1\right)\left(3m+1\right), the least common multiple of 1+3m,1-3m,1-9m^{2}.

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

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

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

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

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

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

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

Add -1 and 1 to get 0.

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

Combine m and m to get 2m.

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

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

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

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

$$2m=-3m+14$$

Add 3m to both sides.

$$2m+3m=14$$

Combine 2m and 3m to get 5m.

$$5m=14$$

Divide both sides by 5.

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