Solve 12x-9/3x-2-4x-5/2x-3=2

$$\frac{ 12x-9 }{ 3x-2 } - \frac{ 4x-5 }{ 2x-3 } =2$$

Solve for x

$$x=1$$

Steps for Solving Linear Equation

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

$$\left(2x-3\right)\left(12x-9\right)-\left(3x-2\right)\left(4x-5\right)=2\left(2x-3\right)\left(3x-2\right)$$

Use the distributive property to multiply 2x-3 by 12x-9 and combine like terms.

$$24x^{2}-54x+27-\left(3x-2\right)\left(4x-5\right)=2\left(2x-3\right)\left(3x-2\right)$$

Use the distributive property to multiply 3x-2 by 4x-5 and combine like terms.

$$24x^{2}-54x+27-\left(12x^{2}-23x+10\right)=2\left(2x-3\right)\left(3x-2\right)$$

To find the opposite of 12x^{2}-23x+10, find the opposite of each term.

$$24x^{2}-54x+27-12x^{2}+23x-10=2\left(2x-3\right)\left(3x-2\right)$$

Combine 24x^{2} and -12x^{2} to get 12x^{2}.

$$12x^{2}-54x+27+23x-10=2\left(2x-3\right)\left(3x-2\right)$$

Combine -54x and 23x to get -31x.

$$12x^{2}-31x+27-10=2\left(2x-3\right)\left(3x-2\right)$$

Subtract 10 from 27 to get 17.

$$12x^{2}-31x+17=2\left(2x-3\right)\left(3x-2\right)$$

Use the distributive property to multiply 2 by 2x-3.

$$12x^{2}-31x+17=\left(4x-6\right)\left(3x-2\right)$$

Use the distributive property to multiply 4x-6 by 3x-2 and combine like terms.

$$12x^{2}-31x+17=12x^{2}-26x+12$$

Subtract 12x^{2} from both sides.

$$12x^{2}-31x+17-12x^{2}=-26x+12$$

Combine 12x^{2} and -12x^{2} to get 0.

$$-31x+17=-26x+12$$

Add 26x to both sides.

$$-31x+17+26x=12$$

Combine -31x and 26x to get -5x.

$$-5x+17=12$$

Subtract 17 from both sides.

$$-5x=12-17$$

Subtract 17 from 12 to get -5.

$$-5x=-5$$

Divide both sides by -5.

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

Divide -5 by -5 to get 1.

$$x=1$$