Standard+2.7a-aa

Standard 2.7a.-aa: Solving Rational Equations
Solving refers to figuring out the variable by eliminating and other methods. A rational equation is two expressions that are equivalent to each other. Also, it is a polynomial fraction. When solving for rational equations, the student will use the relationships among the solution of the quation and factors of a rational expression to solve rational equations.

Example Problems for Standard 2.7a
Below are two example problems. What value of x makes this equation true?** __2__  __3__ x-1 + x+1 The rational expression Two over a number subtracted by one, is added to Three over a number plus one. In order to find the number, we must cross multiply. This means multiplying the terms opposite and across from one another. See the steps below.
 * Problem One:

__2__ __3__ x-1 + x+1 2(x +1) = 3(x-1) cross multiply 2x + 2 = 3x - 3 distribute terms 2x + 2 = 3x - 3 -2x -2x Subtract like terms 2 = x-3 +3 = +3 Add three, 5=x Evaluate 2x=** **__4x+5__ 3 What is the value of x?**
 * ProblemTwo

This problem is only difficult because only one side of the equation has a polynomial fraction. This problem is stating x multiplied by 2 is equal to 4 mulitplied by a number plus five, divided by three.

3 __2x__**  __4x+5__ 1 = 3 3(2x)= 1(4x+5) cross multiply 6+3x= 4x+5 distribute terms 7x+5=6 combine like terms 7x=1 subtract like terms
 * 2x=** **__4x+5__

Podcast for Standard 2.7
Below is a tutorial on understanding ration expressions and how to solve them.