Solve [4(h+x)^2-16/(h+x)-2]-[4x^2-16/x-2]

$$[ \frac { 4 ( h + x ) ^ { 2 } - 16 } { ( h + x ) - 2 } ] - [ \frac { 4 x ^ { 2 } - 16 } { x - 2 } ]$$

Evaluate

$$4h$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{4\left(h+x\right)^{2}-16}{h+x-2}.

$$\frac{4\left(x+h-2\right)\left(x+h+2\right)}{x+h-2}-\frac{4x^{2}-16}{x-2}$$

Cancel out x+h-2 in both numerator and denominator.

$$4\left(x+h+2\right)-\frac{4x^{2}-16}{x-2}$$

Expand the expression.

$$4x+4h+8-\frac{4x^{2}-16}{x-2}$$

Factor the expressions that are not already factored in \frac{4x^{2}-16}{x-2}.

$$4x+4h+8-\frac{4\left(x-2\right)\left(x+2\right)}{x-2}$$

Cancel out x-2 in both numerator and denominator.

$$4x+4h+8-4\left(x+2\right)$$

Expand the expression.

$$4x+4h+8-\left(4x+8\right)$$

To find the opposite of 4x+8, find the opposite of each term.

$$4x+4h+8-4x-8$$

Combine 4x and -4x to get 0.

$$4h+8-8$$

Subtract 8 from 8 to get 0.

$$4h$$

Expand

$$4h$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{4\left(h+x\right)^{2}-16}{h+x-2}.

$$\frac{4\left(x+h-2\right)\left(x+h+2\right)}{x+h-2}-\frac{4x^{2}-16}{x-2}$$

Cancel out x+h-2 in both numerator and denominator.

$$4\left(x+h+2\right)-\frac{4x^{2}-16}{x-2}$$

Expand the expression.

$$4x+4h+8-\frac{4x^{2}-16}{x-2}$$

Factor the expressions that are not already factored in \frac{4x^{2}-16}{x-2}.

$$4x+4h+8-\frac{4\left(x-2\right)\left(x+2\right)}{x-2}$$

Cancel out x-2 in both numerator and denominator.

$$4x+4h+8-4\left(x+2\right)$$

Expand the expression.

$$4x+4h+8-\left(4x+8\right)$$

To find the opposite of 4x+8, find the opposite of each term.

$$4x+4h+8-4x-8$$

Combine 4x and -4x to get 0.

$$4h+8-8$$

Subtract 8 from 8 to get 0.

$$4h$$