Multiplying
& Dividing Rational Expressions
Multiplying
& Dividing Rational Expressions
An example of Multiplying
Rational Expressions could look like the problem below. Follow the example
and we will teach you how to complete the problem by using your hand.
y2 +6y * 10-5y
3y2
+ 6y – 24 -10y
1. Factor
each part of the problem.
y2
+6y = y(y+6)
10-5y
= -5(y-2)
3y2
+ 6y – 24 = 3(y2 + 2y – 8) = 3(y + 4)(y – 2)
-10y
cannot be factored
Notice how on the third factored part had to
go an extra step. That is because after factoring it the first time it could
still be factored down some more. Now your problem should look like:
y(y+6) *
-5(y-2)
3(y+4)(y-2) -10y
2.
Now you can cancel out common things, for example in the denominator of the
first part there is a (y-2) and in the numerator of the second part there is
also a (y-2) so you can cross them out. On the right below is an example of
crossing out the common things and on the left is what the problem has been
reduced down to.
y(y+6) * -5(y-2) (y+6) *
1
3(y+4)(y-2) -10y 3(y+4) 2
3. Now you can solve
the rest of the problem by multiplying the numerators together and the
denominators together. The final answer is below.
(y+6)
6(y+4)
To
Divide Rational Expressions by hand is very simple if you know how to
multiply rational expressions. There is only one extra step added at the
beginning. All you do is take the second half of the problem and flip the
numerator with the denominator. An example is shown below.
5a + 25 / 2a2
– 2a – 60
4a
– 12 a2 – 3a
5a
+ 25 /
a2 – 3a
4a
– 12 2a2 – 2a – 60
Multiplying
& Dividing Rational Expressions
Home Solving Multiplying &
Dividing