Solve 4/x-4-2/x+3=-1/x^2-x-12

$$\frac { 4 } { x - 4 } - \frac { 2 } { x + 3 } = - \frac { 1 } { x ^ { 2 } - x - 12 }$$

Solve for x

$$x = -\frac{21}{2} = -10\frac{1}{2} = -10.5$$

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 \left(x-4\right)\left(x+3\right), the least common multiple of x-4,x+3,x^{2}-x-12.

$$\left(x+3\right)\times 4-\left(x-4\right)\times 2=-1$$

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

$$4x+12-\left(x-4\right)\times 2=-1$$

Use the distributive property to multiply x-4 by 2.

$$4x+12-\left(2x-8\right)=-1$$

To find the opposite of 2x-8, find the opposite of each term.

$$4x+12-2x+8=-1$$

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

$$2x+12+8=-1$$

Add 12 and 8 to get 20.

$$2x+20=-1$$

Subtract 20 from both sides.

$$2x=-1-20$$

Subtract 20 from -1 to get -21.

$$2x=-21$$

Divide both sides by 2.

$$x=\frac{-21}{2}$$

Fraction \frac{-21}{2} can be rewritten as -\frac{21}{2} by extracting the negative sign.

$$x=-\frac{21}{2}$$