Solve (1/x+1-x-2/x^2-1)div1/x+1quad1/2yx=(20019-pi)^2+1

$$( \frac { 1 } { x + 1 } - \frac { x - 2 } { x ^ { 2 } - 1 } ) \div \frac { 1 } { x + 1 } \quad \frac { 1 } { 2 } y x = ( 20019 - \pi ) ^ { 2 } + 1$$

Solve for y (complex solution)

$$y=-\frac{2\left(-\pi ^{2}x+40038\pi x-400760362x+\pi ^{2}[phone]\pi \right)}{x}$$

$$x\neq 0\text{ and }x\neq 1\text{ and }x\neq -1$$

Steps for Solving Linear Equation

Factor x^{2}-1.

$$\frac{\frac{1}{x+1}-\frac{x-2}{\left(x-1\right)\left(x+1\right)}}{\frac{1}{x+1}}\times \frac{1}{2}yx=\left(20019-\pi \right)^{2}+1$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x+1 and \left(x-1\right)\left(x+1\right) is \left(x-1\right)\left(x+1\right). Multiply \frac{1}{x+1} times \frac{x-1}{x-1}.

$$\frac{\frac{x-1}{\left(x-1\right)\left(x+1\right)}-\frac{x-2}{\left(x-1\right)\left(x+1\right)}}{\frac{1}{x+1}}\times \frac{1}{2}yx=\left(20019-\pi \right)^{2}+1$$

Since \frac{x-1}{\left(x-1\right)\left(x+1\right)} and \frac{x-2}{\left(x-1\right)\left(x+1\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{x-1-\left(x-2\right)}{\left(x-1\right)\left(x+1\right)}}{\frac{1}{x+1}}\times \frac{1}{2}yx=\left(20019-\pi \right)^{2}+1$$

Do the multiplications in x-1-\left(x-2\right).

$$\frac{\frac{x-1-x+2}{\left(x-1\right)\left(x+1\right)}}{\frac{1}{x+1}}\times \frac{1}{2}yx=\left(20019-\pi \right)^{2}+1$$

Combine like terms in x-1-x+2.

$$\frac{\frac{1}{\left(x-1\right)\left(x+1\right)}}{\frac{1}{x+1}}\times \frac{1}{2}yx=\left(20019-\pi \right)^{2}+1$$

Divide \frac{1}{\left(x-1\right)\left(x+1\right)} by \frac{1}{x+1} by multiplying \frac{1}{\left(x-1\right)\left(x+1\right)} by the reciprocal of \frac{1}{x+1}.

$$\frac{x+1}{\left(x-1\right)\left(x+1\right)}\times \frac{1}{2}yx=\left(20019-\pi \right)^{2}+1$$

Cancel out x+1 in both numerator and denominator.

$$\frac{1}{x-1}\times \frac{1}{2}yx=\left(20019-\pi \right)^{2}+1$$

Multiply \frac{1}{x-1} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{\left(x-1\right)\times 2}yx=\left(20019-\pi \right)^{2}+1$$

Express \frac{1}{\left(x-1\right)\times 2}y as a single fraction.

$$\frac{y}{\left(x-1\right)\times 2}x=\left(20019-\pi \right)^{2}+1$$

Express \frac{y}{\left(x-1\right)\times 2}x as a single fraction.

$$\frac{yx}{\left(x-1\right)\times 2}=\left(20019-\pi \right)^{2}+1$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(20019-\pi \right)^{2}.

$$\frac{yx}{\left(x-1\right)\times 2}=400760361-40038\pi +\pi ^{2}+1$$

Add 400760361 and 1 to get 400760362.

$$\frac{yx}{\left(x-1\right)\times 2}=400760362-40038\pi +\pi ^{2}$$

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

$$\frac{yx}{2x-2}=400760362-40038\pi +\pi ^{2}$$

Multiply both sides of the equation by 2\left(x-1\right).

$$yx=2\left(x-1\right)\times 400760362-40038\pi \times 2\left(x-1\right)+2\left(x-1\right)\pi ^{2}$$

Reorder the terms.

$$xy=2\pi ^{2}\left(x-1\right)-40038\times 2\pi \left(x-1\right)+2\times 400760362\left(x-1\right)$$

Do the multiplications.

$$xy=2\pi ^{2}\left(x-1\right)-80076\pi \left(x-1\right)[phone]\left(x-1\right)$$

Use the distributive property to multiply 2\pi ^{2} by x-1.

$$xy=2\pi ^{2}x-2\pi ^{2}-80076\pi \left(x-1\right)[phone]\left(x-1\right)$$

Use the distributive property to multiply -80076\pi by x-1.

$$xy=2\pi ^{2}x-2\pi ^{2}-80076\pi x+80076\pi [phone]\left(x-1\right)$$

Use the distributive property to multiply 801520724 by x-1.

$$xy=2\pi ^{2}x-2\pi ^{2}-80076\pi x+80076\pi [phone]x-801520724$$

The equation is in standard form.

$$xy=2\pi ^{2}x-80076\pi x+801520724x-2\pi ^{2}+80076\pi -801520724$$

Divide both sides by x.

$$\frac{xy}{x}=\frac{2\pi ^{2}x-80076\pi x+801520724x-2\pi ^{2}+80076\pi -801520724}{x}$$

Dividing by x undoes the multiplication by x.

$$y=\frac{2\pi ^{2}x-80076\pi x+801520724x-2\pi ^{2}+80076\pi -801520724}{x}$$

Divide 2\pi ^{2}x-2\pi ^{2}-80076\pi x+80076\pi [phone]x-801520724 by x.

$$y=\frac{2\left(\pi ^{2}x-40038\pi x+400760362x-\pi ^{2}+40038\pi -400760362\right)}{x}$$

Solve for y

$$y=-\frac{2\left(-\pi ^{2}x+40038\pi x-400760362x+\pi ^{2}[phone]\pi \right)}{x}$$

$$x\neq 0\text{ and }|x|\neq 1$$

Steps for Solving Linear Equation

Factor x^{2}-1.

$$\frac{\frac{1}{x+1}-\frac{x-2}{\left(x-1\right)\left(x+1\right)}}{\frac{1}{x+1}}\times \frac{1}{2}yx=\left(20019-\pi \right)^{2}+1$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x+1 and \left(x-1\right)\left(x+1\right) is \left(x-1\right)\left(x+1\right). Multiply \frac{1}{x+1} times \frac{x-1}{x-1}.

$$\frac{\frac{x-1}{\left(x-1\right)\left(x+1\right)}-\frac{x-2}{\left(x-1\right)\left(x+1\right)}}{\frac{1}{x+1}}\times \frac{1}{2}yx=\left(20019-\pi \right)^{2}+1$$

Since \frac{x-1}{\left(x-1\right)\left(x+1\right)} and \frac{x-2}{\left(x-1\right)\left(x+1\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{x-1-\left(x-2\right)}{\left(x-1\right)\left(x+1\right)}}{\frac{1}{x+1}}\times \frac{1}{2}yx=\left(20019-\pi \right)^{2}+1$$

Do the multiplications in x-1-\left(x-2\right).

$$\frac{\frac{x-1-x+2}{\left(x-1\right)\left(x+1\right)}}{\frac{1}{x+1}}\times \frac{1}{2}yx=\left(20019-\pi \right)^{2}+1$$

Combine like terms in x-1-x+2.

$$\frac{\frac{1}{\left(x-1\right)\left(x+1\right)}}{\frac{1}{x+1}}\times \frac{1}{2}yx=\left(20019-\pi \right)^{2}+1$$

Divide \frac{1}{\left(x-1\right)\left(x+1\right)} by \frac{1}{x+1} by multiplying \frac{1}{\left(x-1\right)\left(x+1\right)} by the reciprocal of \frac{1}{x+1}.

$$\frac{x+1}{\left(x-1\right)\left(x+1\right)}\times \frac{1}{2}yx=\left(20019-\pi \right)^{2}+1$$

Cancel out x+1 in both numerator and denominator.

$$\frac{1}{x-1}\times \frac{1}{2}yx=\left(20019-\pi \right)^{2}+1$$

Multiply \frac{1}{x-1} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{\left(x-1\right)\times 2}yx=\left(20019-\pi \right)^{2}+1$$

Express \frac{1}{\left(x-1\right)\times 2}y as a single fraction.

$$\frac{y}{\left(x-1\right)\times 2}x=\left(20019-\pi \right)^{2}+1$$

Express \frac{y}{\left(x-1\right)\times 2}x as a single fraction.

$$\frac{yx}{\left(x-1\right)\times 2}=\left(20019-\pi \right)^{2}+1$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(20019-\pi \right)^{2}.

$$\frac{yx}{\left(x-1\right)\times 2}=400760361-40038\pi +\pi ^{2}+1$$

Add 400760361 and 1 to get 400760362.

$$\frac{yx}{\left(x-1\right)\times 2}=400760362-40038\pi +\pi ^{2}$$

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

$$\frac{yx}{2x-2}=400760362-40038\pi +\pi ^{2}$$

Multiply both sides of the equation by 2\left(x-1\right).

$$yx=2\left(x-1\right)\times 400760362-40038\pi \times 2\left(x-1\right)+2\left(x-1\right)\pi ^{2}$$

Reorder the terms.

$$xy=2\pi ^{2}\left(x-1\right)-40038\times 2\pi \left(x-1\right)+2\times 400760362\left(x-1\right)$$

Do the multiplications.

$$xy=2\pi ^{2}\left(x-1\right)-80076\pi \left(x-1\right)[phone]\left(x-1\right)$$

Use the distributive property to multiply 2\pi ^{2} by x-1.

$$xy=2\pi ^{2}x-2\pi ^{2}-80076\pi \left(x-1\right)[phone]\left(x-1\right)$$

Use the distributive property to multiply -80076\pi by x-1.

$$xy=2\pi ^{2}x-2\pi ^{2}-80076\pi x+80076\pi [phone]\left(x-1\right)$$

Use the distributive property to multiply 801520724 by x-1.

$$xy=2\pi ^{2}x-2\pi ^{2}-80076\pi x+80076\pi [phone]x-801520724$$

The equation is in standard form.

$$xy=2\pi ^{2}x-80076\pi x+801520724x-2\pi ^{2}+80076\pi -801520724$$

Divide both sides by x.

$$\frac{xy}{x}=\frac{2\pi ^{2}x-80076\pi x+801520724x-2\pi ^{2}+80076\pi -801520724}{x}$$

Dividing by x undoes the multiplication by x.

$$y=\frac{2\pi ^{2}x-80076\pi x+801520724x-2\pi ^{2}+80076\pi -801520724}{x}$$

Divide 2\pi ^{2}x-2\pi ^{2}-80076\pi x+80076\pi [phone]x-801520724 by x.

$$y=\frac{2\left(\pi ^{2}x-40038\pi x+400760362x-\pi ^{2}+40038\pi -400760362\right)}{x}$$

Solve for x (complex solution)

$$x=-\frac{2\left(\pi ^{2}[phone]\pi \right)}{y-2\pi ^{2}+80076\pi -801520724}$$

$$y\neq 4\pi ^{2}[phone]-160152\pi \text{ and }y\neq 2\pi ^{2}[phone]\pi \text{ and }y\neq 0$$

Solve for x

$$x=-\frac{2\left(\pi ^{2}[phone]\pi \right)}{y-2\pi ^{2}+80076\pi -801520724}$$

$$y\neq 0\text{ and }y\neq 2\pi ^{2}[phone]\pi \text{ and }y\neq 4\pi ^{2}[phone]-160152\pi$$