Solve x+1/x+3=4-1/x+3

$$\frac { x + 1 } { x + 3 } = 4 - \frac { 1 } { x + 3 }$$

Solve for x

$$x = -\frac{10}{3} = -3\frac{1}{3} \approx -3.333333333$$

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 x+3.

$$x+1=\left(x+3\right)\times 4-1$$

Use the distributive property to multiply x+3 by 4.

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

Subtract 1 from 12 to get 11.

$$x+1=4x+11$$

Subtract 4x from both sides.

$$x+1-4x=11$$

Combine x and -4x to get -3x.

$$-3x+1=11$$

Subtract 1 from both sides.

$$-3x=11-1$$

Subtract 1 from 11 to get 10.

$$-3x=10$$

Divide both sides by -3.

$$x=\frac{10}{-3}$$

Fraction \frac{10}{-3} can be rewritten as -\frac{10}{3} by extracting the negative sign.

$$x=-\frac{10}{3}$$