Solve 1x/x-2x/x+2|14x/2x

$$1 \frac { x } { x - 2 } \frac { x } { x + 2 } | \frac { 14 x } { 2 x }$$

Evaluate

$$\frac{7x^{2}}{x^{2}-4}$$

Short Solution Steps

Cancel out 2x in both numerator and denominator.

$$1\times \frac{x}{x-2}\times \frac{x}{x+2}|7|$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of 7 is 7.

$$1\times \frac{x}{x-2}\times \frac{x}{x+2}\times 7$$

Multiply 1 and 7 to get 7.

$$7\times \frac{x}{x-2}\times \frac{x}{x+2}$$

Express 7\times \frac{x}{x-2} as a single fraction.

$$\frac{7x}{x-2}\times \frac{x}{x+2}$$

Multiply \frac{7x}{x-2} times \frac{x}{x+2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7xx}{\left(x-2\right)\left(x+2\right)}$$

Multiply x and x to get x^{2}.

$$\frac{7x^{2}}{\left(x-2\right)\left(x+2\right)}$$

Consider \left(x-2\right)\left(x+2\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{7x^{2}}{x^{2}-2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{7x^{2}}{x^{2}-4}$$

Factor

$$\frac{7x^{2}}{x^{2}-4}$$