Solve 2-4x+3/x+x^2=2x/x+1-5/x

$$2 - \frac { 4 x + 3 } { x + x ^ { 2 } } = \frac { 2 x } { x + 1 } - \frac { 5 } { x }$$

Solve for x

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

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -1,0 since division by zero is not defined. Multiply both sides of the equation by x\left(x+1\right), the least common multiple of x+x^{2},x+1,x.

$$x\left(x+1\right)\times 2-\left(4x+3\right)=x\times 2x-\left(x+1\right)\times 5$$

Use the distributive property to multiply x by x+1.

$$\left(x^{2}+x\right)\times 2-\left(4x+3\right)=x\times 2x-\left(x+1\right)\times 5$$

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

$$2x^{2}+2x-\left(4x+3\right)=x\times 2x-\left(x+1\right)\times 5$$

To find the opposite of 4x+3, find the opposite of each term.

$$2x^{2}+2x-4x-3=x\times 2x-\left(x+1\right)\times 5$$

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

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

Multiply x and x to get x^{2}.

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

Use the distributive property to multiply x+1 by 5.

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

To find the opposite of 5x+5, find the opposite of each term.

$$2x^{2}-2x-3=x^{2}\times 2-5x-5$$

Subtract x^{2}\times 2 from both sides.

$$2x^{2}-2x-3-x^{2}\times 2=-5x-5$$

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

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

Add 5x to both sides.

$$-2x-3+5x=-5$$

Combine -2x and 5x to get 3x.

$$3x-3=-5$$

Add 3 to both sides.

$$3x=-5+3$$

Add -5 and 3 to get -2.

$$3x=-2$$

Divide both sides by 3.

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

Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

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