Solve 13{left(x+1/x-1right)}^2+36

$$13 { \left( \frac{ x+1 }{ x-1 } \right) }^{ 2 } +36$$

Evaluate

$$\frac{49x^{2}-46x+49}{\left(x-1\right)^{2}}$$

Short Solution Steps

To raise \frac{x+1}{x-1} to a power, raise both numerator and denominator to the power and then divide.

$$13\times \frac{\left(x+1\right)^{2}}{\left(x-1\right)^{2}}+36$$

Express 13\times \frac{\left(x+1\right)^{2}}{\left(x-1\right)^{2}} as a single fraction.

$$\frac{13\left(x+1\right)^{2}}{\left(x-1\right)^{2}}+36$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 36 times \frac{\left(x-1\right)^{2}}{\left(x-1\right)^{2}}.

$$\frac{13\left(x+1\right)^{2}}{\left(x-1\right)^{2}}+\frac{36\left(x-1\right)^{2}}{\left(x-1\right)^{2}}$$

Since \frac{13\left(x+1\right)^{2}}{\left(x-1\right)^{2}} and \frac{36\left(x-1\right)^{2}}{\left(x-1\right)^{2}} have the same denominator, add them by adding their numerators.

$$\frac{13\left(x+1\right)^{2}+36\left(x-1\right)^{2}}{\left(x-1\right)^{2}}$$

Do the multiplications in 13\left(x+1\right)^{2}+36\left(x-1\right)^{2}.

$$\frac{13x^{2}+26x+13+36x^{2}-72x+36}{\left(x-1\right)^{2}}$$

Combine like terms in 13x^{2}+26x+13+36x^{2}-72x+36.

$$\frac{49x^{2}-46x+49}{\left(x-1\right)^{2}}$$

Expand \left(x-1\right)^{2}.

$$\frac{49x^{2}-46x+49}{x^{2}-2x+1}$$

Expand

$$\frac{49x^{2}-46x+49}{\left(x-1\right)^{2}}$$

Short Solution Steps

To raise \frac{x+1}{x-1} to a power, raise both numerator and denominator to the power and then divide.

$$13\times \frac{\left(x+1\right)^{2}}{\left(x-1\right)^{2}}+36$$

Express 13\times \frac{\left(x+1\right)^{2}}{\left(x-1\right)^{2}} as a single fraction.

$$\frac{13\left(x+1\right)^{2}}{\left(x-1\right)^{2}}+36$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 36 times \frac{\left(x-1\right)^{2}}{\left(x-1\right)^{2}}.

$$\frac{13\left(x+1\right)^{2}}{\left(x-1\right)^{2}}+\frac{36\left(x-1\right)^{2}}{\left(x-1\right)^{2}}$$

Since \frac{13\left(x+1\right)^{2}}{\left(x-1\right)^{2}} and \frac{36\left(x-1\right)^{2}}{\left(x-1\right)^{2}} have the same denominator, add them by adding their numerators.

$$\frac{13\left(x+1\right)^{2}+36\left(x-1\right)^{2}}{\left(x-1\right)^{2}}$$

Do the multiplications in 13\left(x+1\right)^{2}+36\left(x-1\right)^{2}.

$$\frac{13x^{2}+26x+13+36x^{2}-72x+36}{\left(x-1\right)^{2}}$$

Combine like terms in 13x^{2}+26x+13+36x^{2}-72x+36.

$$\frac{49x^{2}-46x+49}{\left(x-1\right)^{2}}$$

Expand \left(x-1\right)^{2}.

$$\frac{49x^{2}-46x+49}{x^{2}-2x+1}$$