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

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

Solve for x

$$x = -\frac{11}{3} = -3\frac{2}{3} \approx -3.666666667$$

Steps for Solving Linear Equation

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

$$\left(x+3\right)\left(-2\right)=\left(x+4\right)\times 4$$

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

$$-2x-6=\left(x+4\right)\times 4$$

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

$$-2x-6=4x+16$$

Subtract 4x from both sides.

$$-2x-6-4x=16$$

Combine -2x and -4x to get -6x.

$$-6x-6=16$$

Add 6 to both sides.

$$-6x=16+6$$

Add 16 and 6 to get 22.

$$-6x=22$$

Divide both sides by -6.

$$x=\frac{22}{-6}$$

Reduce the fraction \frac{22}{-6} to lowest terms by extracting and canceling out 2.

$$x=-\frac{11}{3}$$