Solve ((1)7x/x-3-1=2(3x-1)/x+2

$$( ( 1 ) \frac { 7 x } { x - 3 } - 1 = \frac { 2 ( 3 x - 1 ) } { x + 2 }$$

Solve for x

$$x=0$$

Steps for Solving Linear Equation

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

$$1\left(x+2\right)\times 7x+\left(x-3\right)\left(x+2\right)\left(-1\right)=\left(x-3\right)\times 2\left(3x-1\right)$$

Multiply 1 and 7 to get 7.

$$7\left(x+2\right)x+\left(x-3\right)\left(x+2\right)\left(-1\right)=\left(x-3\right)\times 2\left(3x-1\right)$$

Use the distributive property to multiply 7 by x+2.

$$\left(7x+14\right)x+\left(x-3\right)\left(x+2\right)\left(-1\right)=\left(x-3\right)\times 2\left(3x-1\right)$$

Use the distributive property to multiply 7x+14 by x.

$$7x^{2}+14x+\left(x-3\right)\left(x+2\right)\left(-1\right)=\left(x-3\right)\times 2\left(3x-1\right)$$

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

$$7x^{2}+14x+\left(x^{2}-x-6\right)\left(-1\right)=\left(x-3\right)\times 2\left(3x-1\right)$$

Use the distributive property to multiply x^{2}-x-6 by -1.

$$7x^{2}+14x-x^{2}+x+6=\left(x-3\right)\times 2\left(3x-1\right)$$

Combine 7x^{2} and -x^{2} to get 6x^{2}.

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

Combine 14x and x to get 15x.

$$6x^{2}+15x+6=\left(x-3\right)\times 2\left(3x-1\right)$$

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

$$6x^{2}+15x+6=\left(2x-6\right)\left(3x-1\right)$$

Use the distributive property to multiply 2x-6 by 3x-1 and combine like terms.

$$6x^{2}+15x+6=6x^{2}-20x+6$$

Subtract 6x^{2} from both sides.

$$6x^{2}+15x+6-6x^{2}=-20x+6$$

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

$$15x+6=-20x+6$$

Add 20x to both sides.

$$15x+6+20x=6$$

Combine 15x and 20x to get 35x.

$$35x+6=6$$

Subtract 6 from both sides.

$$35x=6-6$$

Subtract 6 from 6 to get 0.

$$35x=0$$

Product of two numbers is equal to 0 if at least one of them is 0. Since 35 is not equal to 0, x must be equal to 0.

$$x=0$$