Solve x+3/x-2-2x+5/2x-4=3+2/2

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

Solve for x

$$x = \frac{17}{8} = 2\frac{1}{8} = 2.125$$

Steps for Solving Linear Equation

Variable x cannot be equal to 2 since division by zero is not defined. Multiply both sides of the equation by 2\left(x-2\right), the least common multiple of x-2,2x-4,2.

$$2\left(x+3\right)-\left(2x+5\right)=2\left(x-2\right)\times 3+\left(x-2\right)\times 2$$

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

$$2x+6-\left(2x+5\right)=2\left(x-2\right)\times 3+\left(x-2\right)\times 2$$

To find the opposite of 2x+5, find the opposite of each term.

$$2x+6-2x-5=2\left(x-2\right)\times 3+\left(x-2\right)\times 2$$

Combine 2x and -2x to get 0.

$$6-5=2\left(x-2\right)\times 3+\left(x-2\right)\times 2$$

Subtract 5 from 6 to get 1.

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

Multiply 2 and 3 to get 6.

$$1=6\left(x-2\right)+\left(x-2\right)\times 2$$

Use the distributive property to multiply 6 by x-2.

$$1=6x-12+\left(x-2\right)\times 2$$

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

$$1=6x-12+2x-4$$

Combine 6x and 2x to get 8x.

$$1=8x-12-4$$

Subtract 4 from -12 to get -16.

$$1=8x-16$$

Swap sides so that all variable terms are on the left hand side.

$$8x-16=1$$

Add 16 to both sides.

$$8x=1+16$$

Add 1 and 16 to get 17.

$$8x=17$$

Divide both sides by 8.

$$x=\frac{17}{8}$$