Solve x+2/x-2+x-2/x+2=26/5

$$\frac { x + 2 } { x - 2 } + \frac { x - 2 } { x + 2 } = \frac { 26 } { 5 }$$

Solve for x

$$x=3$$

$$x=-3$$

Steps by Finding Square Root

Variable x cannot be equal to any of the values -2,2 since division by zero is not defined. Multiply both sides of the equation by 5\left(x-2\right)\left(x+2\right), the least common multiple of x-2,x+2,5.

$$\left(5x+10\right)\left(x+2\right)+\left(5x-10\right)\left(x-2\right)=26\left(x-2\right)\left(x+2\right)$$

Use the distributive property to multiply 5x+10 by x+2 and combine like terms.

$$5x^{2}+20x+20+\left(5x-10\right)\left(x-2\right)=26\left(x-2\right)\left(x+2\right)$$

Use the distributive property to multiply 5x-10 by x-2 and combine like terms.

$$5x^{2}+20x+20+5x^{2}-20x+20=26\left(x-2\right)\left(x+2\right)$$

Combine 5x^{2} and 5x^{2} to get 10x^{2}.

$$10x^{2}+20x+20-20x+20=26\left(x-2\right)\left(x+2\right)$$

Combine 20x and -20x to get 0.

$$10x^{2}+20+20=26\left(x-2\right)\left(x+2\right)$$

Add 20 and 20 to get 40.

$$10x^{2}+40=26\left(x-2\right)\left(x+2\right)$$

Use the distributive property to multiply 26 by x-2.

$$10x^{2}+40=\left(26x-52\right)\left(x+2\right)$$

Use the distributive property to multiply 26x-52 by x+2 and combine like terms.

$$10x^{2}+40=26x^{2}-104$$

Subtract 26x^{2} from both sides.

$$10x^{2}+40-26x^{2}=-104$$

Combine 10x^{2} and -26x^{2} to get -16x^{2}.

$$-16x^{2}+40=-104$$

Subtract 40 from both sides.

$$-16x^{2}=-104-40$$

Subtract 40 from -104 to get -144.

$$-16x^{2}=-144$$

Divide both sides by -16.

$$x^{2}=\frac{-144}{-16}$$

Divide -144 by -16 to get 9.

$$x^{2}=9$$

Take the square root of both sides of the equation.

$$x=3 x=-3$$

Steps Using the Quadratic Formula

Variable x cannot be equal to any of the values -2,2 since division by zero is not defined. Multiply both sides of the equation by 5\left(x-2\right)\left(x+2\right), the least common multiple of x-2,x+2,5.

$$\left(5x+10\right)\left(x+2\right)+\left(5x-10\right)\left(x-2\right)=26\left(x-2\right)\left(x+2\right)$$

Use the distributive property to multiply 5x+10 by x+2 and combine like terms.

$$5x^{2}+20x+20+\left(5x-10\right)\left(x-2\right)=26\left(x-2\right)\left(x+2\right)$$

Use the distributive property to multiply 5x-10 by x-2 and combine like terms.

$$5x^{2}+20x+20+5x^{2}-20x+20=26\left(x-2\right)\left(x+2\right)$$

Combine 5x^{2} and 5x^{2} to get 10x^{2}.

$$10x^{2}+20x+20-20x+20=26\left(x-2\right)\left(x+2\right)$$

Combine 20x and -20x to get 0.

$$10x^{2}+20+20=26\left(x-2\right)\left(x+2\right)$$

Add 20 and 20 to get 40.

$$10x^{2}+40=26\left(x-2\right)\left(x+2\right)$$

Use the distributive property to multiply 26 by x-2.

$$10x^{2}+40=\left(26x-52\right)\left(x+2\right)$$

Use the distributive property to multiply 26x-52 by x+2 and combine like terms.

$$10x^{2}+40=26x^{2}-104$$

Subtract 26x^{2} from both sides.

$$10x^{2}+40-26x^{2}=-104$$

Combine 10x^{2} and -26x^{2} to get -16x^{2}.

$$-16x^{2}+40=-104$$

Add 104 to both sides.

$$-16x^{2}+40+104=0$$

Add 40 and 104 to get 144.

$$-16x^{2}+144=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -16 for a, 0 for b, and 144 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-16\right)\times 144}}{2\left(-16\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-16\right)\times 144}}{2\left(-16\right)}$$

Multiply -4 times -16.

$$x=\frac{0±\sqrt{64\times 144}}{2\left(-16\right)}$$

Multiply 64 times 144.

$$x=\frac{0±\sqrt{9216}}{2\left(-16\right)}$$

Take the square root of 9216.

$$x=\frac{0±96}{2\left(-16\right)}$$

Multiply 2 times -16.

$$x=\frac{0±96}{-32}$$

Now solve the equation x=\frac{0±96}{-32} when ± is plus. Divide 96 by -32.

$$x=-3$$

Now solve the equation x=\frac{0±96}{-32} when ± is minus. Divide -96 by -32.

$$x=3$$

The equation is now solved.

$$x=-3 x=3$$