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

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

Solve for x

$$x=2$$

$$x=-2$$

Steps by Finding Square Root

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+1.

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

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

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

Use the distributive property to multiply 2x by x+1.

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

Subtract 2x^{2} from both sides.

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

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

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

Subtract 2x from both sides.

$$-x^{2}+5x+4-x\times 3-2x=0$$

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

$$-x^{2}+3x+4-x\times 3=0$$

Subtract 4 from both sides. Anything subtracted from zero gives its negation.

$$-x^{2}+3x-x\times 3=-4$$

Multiply -1 and 3 to get -3.

$$-x^{2}+3x-3x=-4$$

Combine 3x and -3x to get 0.

$$-x^{2}=-4$$

Divide both sides by -1.

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

Fraction \frac{-4}{-1} can be simplified to 4 by removing the negative sign from both the numerator and the denominator.

$$x^{2}=4$$

Take the square root of both sides of the equation.

$$x=2 x=-2$$

Steps Using the Quadratic Formula

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+1.

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

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

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

Use the distributive property to multiply 2x by x+1.

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

Subtract 2x^{2} from both sides.

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

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

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

Subtract 2x from both sides.

$$-x^{2}+5x+4-x\times 3-2x=0$$

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

$$-x^{2}+3x+4-x\times 3=0$$

Multiply -1 and 3 to get -3.

$$-x^{2}+3x+4-3x=0$$

Combine 3x and -3x to get 0.

$$-x^{2}+4=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 0 for b, and 4 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\times 4}}{2\left(-1\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1\right)\times 4}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{0±\sqrt{4\times 4}}{2\left(-1\right)}$$

Multiply 4 times 4.

$$x=\frac{0±\sqrt{16}}{2\left(-1\right)}$$

Take the square root of 16.

$$x=\frac{0±4}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{0±4}{-2}$$

Now solve the equation x=\frac{0±4}{-2} when ± is plus. Divide 4 by -2.

$$x=-2$$

Now solve the equation x=\frac{0±4}{-2} when ± is minus. Divide -4 by -2.

$$x=2$$

The equation is now solved.

$$x=-2 x=2$$