Solve 1/x+3-2/5x-20=3/2(3x-12)-2/x+3

$$\frac { 1 } { x + 3 } - \frac { 2 } { 5 x - 20 } = \frac { 3 } { 2 ( 3 x - 12 ) } - \frac { 2 } { x + 3 }$$

Solve for x

$$x=7$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -3,4 since division by zero is not defined. Multiply both sides of the equation by 30\left(x-4\right)\left(x+3\right), the least common multiple of x+3,5x-20,2\left(3x-12\right).

$$30x-120-\left(6x+18\right)\times 2=\left(5x+15\right)\times 3-\left(30x-120\right)\times 2$$

Use the distributive property to multiply 6x+18 by 2.

$$30x-120-\left(12x+36\right)=\left(5x+15\right)\times 3-\left(30x-120\right)\times 2$$

To find the opposite of 12x+36, find the opposite of each term.

$$30x-120-12x-36=\left(5x+15\right)\times 3-\left(30x-120\right)\times 2$$

Combine 30x and -12x to get 18x.

$$18x-120-36=\left(5x+15\right)\times 3-\left(30x-120\right)\times 2$$

Subtract 36 from -120 to get -156.

$$18x-156=\left(5x+15\right)\times 3-\left(30x-120\right)\times 2$$

Use the distributive property to multiply 5x+15 by 3.

$$18x-156=15x+45-\left(30x-120\right)\times 2$$

Use the distributive property to multiply 30x-120 by 2.

$$18x-156=15x+45-\left(60x-240\right)$$

To find the opposite of 60x-240, find the opposite of each term.

$$18x-156=15x+45-60x+240$$

Combine 15x and -60x to get -45x.

$$18x-156=-45x+45+240$$

Add 45 and 240 to get 285.

$$18x-156=-45x+285$$

Add 45x to both sides.

$$18x-156+45x=285$$

Combine 18x and 45x to get 63x.

$$63x-156=285$$

Add 156 to both sides.

$$63x=285+156$$

Add 285 and 156 to get 441.

$$63x=441$$

Divide both sides by 63.

$$x=\frac{441}{63}$$

Divide 441 by 63 to get 7.

$$x=7$$