Hi welcome to MooMooMath Today we are going to learn how to simplify expressions with
variables. This expression is a fraction which is another
name for a rational, so sometimes you will hear them called a rational expression, which
are just fractions. Our first example is 24x^5y^6/15x^2y^4
The first thing I will do is create a factor tree for the numerator.
Step one of the factor tree will be 24 breaks down to 4 x 6 which breaks down to 2 x2x2
x3 I will next take those factors and rewrite
them here. Now lets look at the variables of this fraction.
I have x times x times x times x times x which is x to the fifth. I also have six y's because
it is y to the sixth. Those are all of the factors of 24x^5y^6 I will next do the same
thing to the denominator. 15 and draw a factor tree and that is just 5 times 3 and I will
bring that up here. x^2 is x times x, and y^4 is y y y y
Now I get to do the fun part. I get to cancel, because any value divided by itself is one.
The threes will cancel, Two x's cancel, I next go to the y variable and four of them
cancel. What do I have left? I will take all of the factors and multiply them back together
to get my final answer. So 2 x 2 = 4 x 2 = 8 and I have two y's left so I have y^2. In
my denominator the only value I have is the 5 The final answer to this rational expression
is 8x^3y^2/5 or you can write is as 8/5 x^3y^2 Lets try one more rational expressions
Lets create a factor tree of 16 which is 2 x 8 2 x4 and 2 x 2 so we are left with 2 * 2
*2 *2 and a^5 is a*a*a*a*a and b and c to the fifth I will write five c's
This will be my numerator. Lets next take our denominator.
We have 20 which is 2 x 10 and 10 is 2 times 5 so I have 2 *2 *5 in the denominator. Lets
write out our factors for a^2 which is a *a and b^3 is b*b*b, and c ^5 is 5 c's
Now we have our factors so we can now cancel out, because any number divided by itself
is one. Here are all the coefficients I can cancel. I will go to the a's and I can cancel
one, and I can take off one b and I can cancel all of the c's
Lets see what I'm left with. I have 2 on top and another 2 which equals
4, and a cubed and my b is gone, and my c. On the bottom I have a 5 left.
So my final answer is 4a^3/5b^2 So that is my final answer.
Hope this video was helpful on learning how to simplfy expressions with variables