Solve x+2/2-x-x-2/2+x=41/4

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

Solve for x

$$x = -\frac{6}{5} = -1\frac{1}{5} = -1.2$$

$$x = \frac{6}{5} = 1\frac{1}{5} = 1.2$$

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 4\left(x-2\right)\left(x+2\right), the least common multiple of 2-x,2+x,4.

$$\left(-8-4x\right)\left(x+2\right)-\left(4x-8\right)\left(x-2\right)=\left(x^{2}-4\right)\left(4\times 4+1\right)$$

Use the distributive property to multiply -8-4x by x+2 and combine like terms.

$$-16x-16-4x^{2}-\left(4x-8\right)\left(x-2\right)=\left(x^{2}-4\right)\left(4\times 4+1\right)$$

Use the distributive property to multiply 4x-8 by x-2 and combine like terms.

$$-16x-16-4x^{2}-\left(4x^{2}-16x+16\right)=\left(x^{2}-4\right)\left(4\times 4+1\right)$$

To find the opposite of 4x^{2}-16x+16, find the opposite of each term.

$$-16x-16-4x^{2}-4x^{2}+16x-16=\left(x^{2}-4\right)\left(4\times 4+1\right)$$

Combine -4x^{2} and -4x^{2} to get -8x^{2}.

$$-16x-16-8x^{2}+16x-16=\left(x^{2}-4\right)\left(4\times 4+1\right)$$

Combine -16x and 16x to get 0.

$$-16-8x^{2}-16=\left(x^{2}-4\right)\left(4\times 4+1\right)$$

Subtract 16 from -16 to get -32.

$$-32-8x^{2}=\left(x^{2}-4\right)\left(4\times 4+1\right)$$

Multiply 4 and 4 to get 16.

$$-32-8x^{2}=\left(x^{2}-4\right)\left(16+1\right)$$

Add 16 and 1 to get 17.

$$-32-8x^{2}=\left(x^{2}-4\right)\times 17$$

Use the distributive property to multiply x^{2}-4 by 17.

$$-32-8x^{2}=17x^{2}-68$$

Subtract 17x^{2} from both sides.

$$-32-8x^{2}-17x^{2}=-68$$

Combine -8x^{2} and -17x^{2} to get -25x^{2}.

$$-32-25x^{2}=-68$$

Add 32 to both sides.

$$-25x^{2}=-68+32$$

Add -68 and 32 to get -36.

$$-25x^{2}=-36$$

Divide both sides by -25.

$$x^{2}=\frac{-36}{-25}$$

Fraction \frac{-36}{-25} can be simplified to \frac{36}{25} by removing the negative sign from both the numerator and the denominator.

$$x^{2}=\frac{36}{25}$$

Take the square root of both sides of the equation.

$$x=\frac{6}{5} x=-\frac{6}{5}$$

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 4\left(x-2\right)\left(x+2\right), the least common multiple of 2-x,2+x,4.

$$\left(-8-4x\right)\left(x+2\right)-\left(4x-8\right)\left(x-2\right)=\left(x^{2}-4\right)\left(4\times 4+1\right)$$

Use the distributive property to multiply -8-4x by x+2 and combine like terms.

$$-16x-16-4x^{2}-\left(4x-8\right)\left(x-2\right)=\left(x^{2}-4\right)\left(4\times 4+1\right)$$

Use the distributive property to multiply 4x-8 by x-2 and combine like terms.

$$-16x-16-4x^{2}-\left(4x^{2}-16x+16\right)=\left(x^{2}-4\right)\left(4\times 4+1\right)$$

To find the opposite of 4x^{2}-16x+16, find the opposite of each term.

$$-16x-16-4x^{2}-4x^{2}+16x-16=\left(x^{2}-4\right)\left(4\times 4+1\right)$$

Combine -4x^{2} and -4x^{2} to get -8x^{2}.

$$-16x-16-8x^{2}+16x-16=\left(x^{2}-4\right)\left(4\times 4+1\right)$$

Combine -16x and 16x to get 0.

$$-16-8x^{2}-16=\left(x^{2}-4\right)\left(4\times 4+1\right)$$

Subtract 16 from -16 to get -32.

$$-32-8x^{2}=\left(x^{2}-4\right)\left(4\times 4+1\right)$$

Multiply 4 and 4 to get 16.

$$-32-8x^{2}=\left(x^{2}-4\right)\left(16+1\right)$$

Add 16 and 1 to get 17.

$$-32-8x^{2}=\left(x^{2}-4\right)\times 17$$

Use the distributive property to multiply x^{2}-4 by 17.

$$-32-8x^{2}=17x^{2}-68$$

Subtract 17x^{2} from both sides.

$$-32-8x^{2}-17x^{2}=-68$$

Combine -8x^{2} and -17x^{2} to get -25x^{2}.

$$-32-25x^{2}=-68$$

Add 68 to both sides.

$$-32-25x^{2}+68=0$$

Add -32 and 68 to get 36.

$$36-25x^{2}=0$$

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.

$$-25x^{2}+36=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -25 for a, 0 for b, and 36 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-25\right)\times 36}}{2\left(-25\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-25\right)\times 36}}{2\left(-25\right)}$$

Multiply -4 times -25.

$$x=\frac{0±\sqrt{100\times 36}}{2\left(-25\right)}$$

Multiply 100 times 36.

$$x=\frac{0±\sqrt{3600}}{2\left(-25\right)}$$

Take the square root of 3600.

$$x=\frac{0±60}{2\left(-25\right)}$$

Multiply 2 times -25.

$$x=\frac{0±60}{-50}$$

Now solve the equation x=\frac{0±60}{-50} when ± is plus. Reduce the fraction \frac{60}{-50} to lowest terms by extracting and canceling out 10.

$$x=-\frac{6}{5}$$

Now solve the equation x=\frac{0±60}{-50} when ± is minus. Reduce the fraction \frac{-60}{-50} to lowest terms by extracting and canceling out 10.

$$x=\frac{6}{5}$$

The equation is now solved.

$$x=-\frac{6}{5} x=\frac{6}{5}$$