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

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

Solve for x

$$x=\sqrt{6}\approx 2.449489743$$

$$x=-\sqrt{6}\approx -2.449489743$$

Steps by Finding Square Root

Variable x cannot be equal to any of the values -3,0 since division by zero is not defined. Multiply both sides of the equation by x\left(x+3\right), the least common multiple of x,x+3.

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

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

$$2x+6+x=x\left(x+3\right)$$

Combine 2x and x to get 3x.

$$3x+6=x\left(x+3\right)$$

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

$$3x+6=x^{2}+3x$$

Subtract x^{2} from both sides.

$$3x+6-x^{2}=3x$$

Subtract 3x from both sides.

$$3x+6-x^{2}-3x=0$$

Combine 3x and -3x to get 0.

$$6-x^{2}=0$$

Subtract 6 from both sides. Anything subtracted from zero gives its negation.

$$-x^{2}=-6$$

Divide both sides by -1.

$$x^{2}=\frac{-6}{-1}$$

Fraction \frac{-6}{-1} can be simplified to 6 by removing the negative sign from both the numerator and the denominator.

$$x^{2}=6$$

Take the square root of both sides of the equation.

$$x=\sqrt{6} x=-\sqrt{6}$$

Steps Using the Quadratic Formula

Variable x cannot be equal to any of the values -3,0 since division by zero is not defined. Multiply both sides of the equation by x\left(x+3\right), the least common multiple of x,x+3.

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

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

$$2x+6+x=x\left(x+3\right)$$

Combine 2x and x to get 3x.

$$3x+6=x\left(x+3\right)$$

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

$$3x+6=x^{2}+3x$$

Subtract x^{2} from both sides.

$$3x+6-x^{2}=3x$$

Subtract 3x from both sides.

$$3x+6-x^{2}-3x=0$$

Combine 3x and -3x to get 0.

$$6-x^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$-x^{2}+6=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 0 for b, and 6 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\times 6}}{2\left(-1\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1\right)\times 6}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{0±\sqrt{4\times 6}}{2\left(-1\right)}$$

Multiply 4 times 6.

$$x=\frac{0±\sqrt{24}}{2\left(-1\right)}$$

Take the square root of 24.

$$x=\frac{0±2\sqrt{6}}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{0±2\sqrt{6}}{-2}$$

Now solve the equation x=\frac{0±2\sqrt{6}}{-2} when ± is plus.

$$x=-\sqrt{6}$$

Now solve the equation x=\frac{0±2\sqrt{6}}{-2} when ± is minus.

$$x=\sqrt{6}$$

The equation is now solved.

$$x=-\sqrt{6} x=\sqrt{6}$$