Solving Rational Expressions
Solving Rational Expressions
A rational expression that needs to be
solved will contain an equal sign. This means that after the problem has been
solved we will be left with a number, such as y = 5 or b =-51. The equation below is an example of
a problem that will be solved for y.:
7y + 5 = 2y
y^2 - 4 y- 2 y^2 -4
So
lets solve it!
1.
To solve rational expressions begin by factoring out what you can.
7y + 5 = 2y
5y +25 y -2
y^2 - 4
Becomes
7y +
5 = 2y
(
y+2)(y-2) (y-2) (y+2)(y-2)
2.
Notice that the denominators of all the above fractions are not common(
they are not all the same). So in order to be able to add the numerators
together, to solve the problem, we will have to do something to make the
denominators the same.
Start by looking at the denominators to determine
what makes them different from one another. Notice in the example above that
the fraction 5/(y-2) is different from the others. What is different? The
denominator of this fraction would be the same as the other denominators in the
problem if it had this: (y+2). So we must fit this number into its denominator
somehow. The way to do this is to multiply both the top and the bottom of the
incomplete fraction by the missing number, or in this case (y+2). Follow the
example below.
7y
+ 5 =
2y
(y+2)(y-2) (y-2) (y+2) (y-2)
7y + 5y +10 = 2y
(y+2)(y-2) (y+2)(y-2) (y+2) (y-2)
Notice that the denominators of all the fractions are the same. Thus they cancel each other out. Now is also the time to add 7y +5y +10. Now our problem looks like this:
12y + 10 =2y
All we need to do now to solve this problem is
solve the above equation algebraically. Remember we are looking to find the
value of y so we must get it by itself on one side with the other numbers on
the other side of the equal sign.
12y +10 = 2y
-12 -12
10 = -10y
-10
-10
y
= -1
Solving Rational Expressions
Home Multiplying
& Dividing Solving