Lesson 4D: Solving Rational Equations

Muhammad ibn Musa al-Khwarizmi was a Persian mathematician, astronomer, and geographer. In ninth-century Baghdad, he wrote a book entitled Hisab al-jabrw'al-muqabla, or Calculation by Restoration and Reduction.

His book was so influential that, when it was translated into Latin, the al-jabr in the title became algebra. We still use this word today to refer to the math of equations.

In his book, al-Khwarizmi described al-jabr, or restoration, as the process by which the equation

A = B − C becomes A + C = B (Add C to both sides of the equation.)

and reduction as the process by which the equation

A = B + C becomes A − C = B (Subtract C from both sides of the equation.)

You can see that both restoration and reduction are examples of the general rule that whatever you do to one side of an equation you must do to the other as well.

You will use this rule to solve rational equations in this Training Camp.

By the end of this lesson, you should be able to

	determine the non-permissible values for the variable in a rational equation
	determine algebraically, the solution to a rational equation
	explain why a value obtained in solving a rational equation may not be a solution of the equation
	solve a contextual problem that involves a rational equation