Solve -2x/x+1=-2+1/x+4

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

Solve for x

$$x=-7$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -4,-1 since division by zero is not defined. Multiply both sides of the equation by \left(x+1\right)\left(x+4\right), the least common multiple of x+1,x+4.

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

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

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

Use the distributive property to multiply -2x-8 by x.

$$-2x^{2}-8x=\left(x+1\right)\left(x+4\right)\left(-2\right)+x+1$$

Use the distributive property to multiply x+1 by x+4 and combine like terms.

$$-2x^{2}-8x=\left(x^{2}+5x+4\right)\left(-2\right)+x+1$$

Use the distributive property to multiply x^{2}+5x+4 by -2.

$$-2x^{2}-8x=-2x^{2}-10x-8+x+1$$

Combine -10x and x to get -9x.

$$-2x^{2}-8x=-2x^{2}-9x-8+1$$

Add -8 and 1 to get -7.

$$-2x^{2}-8x=-2x^{2}-9x-7$$

Add 2x^{2} to both sides.

$$-2x^{2}-8x+2x^{2}=-9x-7$$

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

$$-8x=-9x-7$$

Add 9x to both sides.

$$-8x+9x=-7$$

Combine -8x and 9x to get x.

$$x=-7$$