Solve {left(sqrt{x+2}right)}^2-{left(sqrt{x-3}right)}^2

$${ \left( \sqrt{ x+2 } \right) }^{ 2 } - { \left( \sqrt{ x-3 } \right) }^{ 2 }$$

Evaluate

$$5$$

Solution Steps

Calculate \sqrt{x+2} to the power of 2 and get x+2.

$$x+2-\left(\sqrt{x-3}\right)^{2}$$

Calculate \sqrt{x-3} to the power of 2 and get x-3.

$$x+2-\left(x-3\right)$$

To find the opposite of x-3, find the opposite of each term.

$$x+2-x+3$$

Combine x and -x to get 0.

$$2+3$$

Add 2 and 3 to get 5.

$$5$$

Factor

$$5$$

Solution Steps

The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(\sqrt{x+2}-\sqrt{x-3}\right)\left(\sqrt{x+2}+\sqrt{x-3}\right)$$