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

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

Solve for x

$$x=\frac{2}{3}\approx 0.666666667$$

Steps for Solving Linear Equation

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

$$2\left(x+3\right)\times \frac{1}{2}-2\times 3=5+2\left(x+3\right)\left(-1\right)$$

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

$$\left(2x+6\right)\times \frac{1}{2}-2\times 3=5+2\left(x+3\right)\left(-1\right)$$

Use the distributive property to multiply 2x+6 by \frac{1}{2}.

$$x+3-2\times 3=5+2\left(x+3\right)\left(-1\right)$$

Multiply -2 and 3 to get -6.

$$x+3-6=5+2\left(x+3\right)\left(-1\right)$$

Subtract 6 from 3 to get -3.

$$x-3=5+2\left(x+3\right)\left(-1\right)$$

Multiply 2 and -1 to get -2.

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

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

$$x-3=5-2x-6$$

Subtract 6 from 5 to get -1.

$$x-3=-1-2x$$

Add 2x to both sides.

$$x-3+2x=-1$$

Combine x and 2x to get 3x.

$$3x-3=-1$$

Add 3 to both sides.

$$3x=-1+3$$

Add -1 and 3 to get 2.

$$3x=2$$

Divide both sides by 3.

$$x=\frac{2}{3}$$