Solve (sqrt{x}+sqrt{x-1})(sqrt{x}-sqrt{x-1})

$$( \sqrt { x } + \sqrt { x - 1 } ) ( \sqrt { x } - \sqrt { x - 1 } )$$

Evaluate

$$1$$

Solution Steps

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

$$\left(\sqrt{x}\right)^{2}-\left(\sqrt{x-1}\right)^{2}$$

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

$$x-\left(\sqrt{x-1}\right)^{2}$$

Calculate \sqrt{x-1} to the power of 2 and get x-1.

$$x-\left(x-1\right)$$

To find the opposite of x-1, find the opposite of each term.

$$x-x-\left(-1\right)$$

The opposite of -1 is 1.

$$x-x+1$$

Combine x and -x to get 0.

$$1$$

Factor

$$1$$