A rational equation is one in which the variable occurs as a rational expression either on one or both sides of an equation. For example,

To solve such equations , simplify each side so that there is only one rational expression on either side. In the present case we may simplify left side to get

So that the equation becomes . Now cross multiply and solve the equation.

(x+1)² = (x-1)(x+2)

Or, x² +2x+1 = x² +x-2

This will give x= -3, which is the required solution. Always verify the solution with the original equation. If it does not satisfy the equation, the solution should be rejected and in that case, the equation will have no solution

***

A radical equation is one in which the variable appears under a radical sign.. For example √(x+5) = x+2.

To solve such an equation, remove the radical sign by squaring on both sides

X+5= (x+2)²

Or, x² +4x+4= x+5

Or x² +3x -1 =0. This can be solved by using quadratic formula,

X=, Or,

****