Solve each equation. See Examples 4–6. √(4x+1)-√(x-1)=2

Key Concepts

Square Roots

Square roots are mathematical operations that find a number which, when multiplied by itself, gives the original number. In the context of the equation, understanding how to manipulate square roots is essential for isolating variables and simplifying expressions. For example, if √a = b, then squaring both sides gives a = b².

Isolating Variables

Isolating variables involves rearranging an equation to get a specific variable on one side. This is crucial in solving equations, especially those involving square roots, as it allows for clearer steps to find the solution. For instance, in the equation √(4x+1) - √(x-1) = 2, isolating one square root can simplify the problem.

Squaring Both Sides

Squaring both sides of an equation is a technique used to eliminate square roots. When both sides of an equation are squared, it can lead to a new equation that is easier to solve. However, it is important to check for extraneous solutions afterward, as squaring can introduce solutions that do not satisfy the original equation.