can someone please help me with my algebra? you don't have to answer every question but I'm very confused, this is algebra 1b unit 6 sample work
simplify the rational expressions. state any excluded values
1. 36x^3 / 42x^2
2. -70n^2 / 28n
3. 2r-4 / r-2
4. 10 / 10a-10
5. x-4 / 3x^2-12x
6. x-5 / x^2-10x+25
7. y+6 / y^2+5y-6
8. x-4 / x^2-16
9. x^2-25 / x+5
10. x^2-5x-14 / x^2+4x+4
I can simplify but have no idea how to find excluded values and I've looked through textbooks and youtube videos but still don't understand. thanks in advance
Excluded values: Division by zero is not allowed.
example:
10. (x^2-5x-14)/(x^2+4x+4)= (x-7)(x+2)/(x+2)^2= (x-7)/(x+2)
x=-2 is excluded, as the denominator would be zero.
7. (y+6)/(y^2+5y-6)= (y+6)/(y+6)(y-1)= 1/(y-1)
y=1 is an excluded value.
but notice on 1, and 2.
1. 36x^3/42x^2=36x/42 No excluded values (the x in denomintor is gone)
On #1, x=0 is excluded, because in the original expression that evaluates to 0/0
Excluded values may appear to vanish as you eliminate common factors, but the initial expression and the final result are equivalent only when those eliminated values are excluded.
36x^3 / 42x^2 = 6x/7 only when x≠0
Sure, I'd be happy to help you with your algebra questions!
To simplify rational expressions, we need to factor the expressions and cancel out any common factors. The excluded values are the values of the variable(s) that make the denominator zero, as division by zero is undefined.
Let's go through each question and explain the steps you can take:
1. 36x^3 / 42x^2
To simplify this expression, we can cancel out the common factors in the numerator and denominator. In this case, both have factors of 6x^2. So, we can simplify it as:
(36x^3) / (42x^2) = (6x^2 * 6x) / (6x^2 * 7) = 6x / 7
The excluded value here is x = 0 since it would make the denominator zero.
2. -70n^2 / 28n
Similarly, we can cancel out the factors of 14n in the numerator and denominator:
(-70n^2) / (28n) = (-14n * 5n) / (4n) = -14n
There are no excluded values here since division by zero is not a concern.
3. 2r-4 / r-2
This expression does not appear to have any common factors, so we cannot cancel anything out. However, we can factor the denominator:
(2r - 4) / (r - 2) = 2(r - 2) / (r - 2)
Now, we have a common factor of (r - 2) in the numerator and denominator, so we can cancel it out:
= 2
The excluded value here is r = 2 since it would make the denominator zero.
4. 10 / (10a - 10)
We can factor out a common factor of 10 in the denominator:
10 / (10a - 10) = 10 / 10(a - 1)
Canceling the common factor of 10, we get:
= 1 / (a - 1)
The excluded value is a = 1 since it would make the denominator zero.
5. (x - 4) / (3x^2 - 12x)
We can factor out a common factor of x in the numerator:
(x - 4) / (3x^2 - 12x) = x(x - 4) / 3x(x - 4)
Notice that (x - 4) appears in both the numerator and denominator. We can cancel it out, but we need to be careful and state the excluded value separately:
= x / 3x
= 1 / 3
The excluded value here is x = 4 since it would make the denominator zero.
6. (x - 5) / (x^2 - 10x + 25)
The denominator here can be factored into a perfect square: (x - 5)^2. So, we have:
(x - 5) / (x^2 - 10x + 25) = (x - 5) / (x - 5)^2
Notice that (x - 5) appears in both the numerator and denominator. We can cancel it out, but we need to state the excluded value separately:
= 1 / (x - 5)
The excluded value here is x = 5 since it would make the denominator zero.
I'll provide steps for the remaining questions in the next response.