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

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

Solve for x

$$x=\sqrt{7}\approx 2.645751311$$

$$x=-\sqrt{7}\approx -2.645751311$$

Steps by Finding Square Root

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

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

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

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

Combine x and -x to get 0.

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

Subtract 3 from -3 to get -6.

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

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

$$-6=\left(3x-9\right)\left(x+3\right)$$

Use the distributive property to multiply 3x-9 by x+3 and combine like terms.

$$-6=3x^{2}-27$$

Swap sides so that all variable terms are on the left hand side.

$$3x^{2}-27=-6$$

Add 27 to both sides.

$$3x^{2}=-6+27$$

Add -6 and 27 to get 21.

$$3x^{2}=21$$

Divide both sides by 3.

$$x^{2}=\frac{21}{3}$$

Divide 21 by 3 to get 7.

$$x^{2}=7$$

Take the square root of both sides of the equation.

$$x=\sqrt{7} x=-\sqrt{7}$$

Steps Using the Quadratic Formula

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

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

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

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

Combine x and -x to get 0.

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

Subtract 3 from -3 to get -6.

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

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

$$-6=\left(3x-9\right)\left(x+3\right)$$

Use the distributive property to multiply 3x-9 by x+3 and combine like terms.

$$-6=3x^{2}-27$$

Swap sides so that all variable terms are on the left hand side.

$$3x^{2}-27=-6$$

Add 6 to both sides.

$$3x^{2}-27+6=0$$

Add -27 and 6 to get -21.

$$3x^{2}-21=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and -21 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-21\right)}}{2\times 3}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 3\left(-21\right)}}{2\times 3}$$

Multiply -4 times 3.

$$x=\frac{0±\sqrt{-12\left(-21\right)}}{2\times 3}$$

Multiply -12 times -21.

$$x=\frac{0±\sqrt{252}}{2\times 3}$$

Take the square root of 252.

$$x=\frac{0±6\sqrt{7}}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{0±6\sqrt{7}}{6}$$

Now solve the equation x=\frac{0±6\sqrt{7}}{6} when ± is plus.

$$x=\sqrt{7}$$

Now solve the equation x=\frac{0±6\sqrt{7}}{6} when ± is minus.

$$x=-\sqrt{7}$$

The equation is now solved.

$$x=\sqrt{7} x=-\sqrt{7}$$