i'm studying for a test on rational expressions and i just wanted to know the answers to some of the problems i am not too sure about...
1... 4y-2/8y-2.. i got 1/2 which restriction of 1/2
2...(x-3/3x-5)/3-x/6x-10.. i got 4 with restrictions of 3 and 5/3
3...3a+6/2a^2+7a+6..1/2a with restrictions of -3/2 and -2
please help:D
I disagree with all 3 of your answers
1. (4y-2)/(8y-2)
= 2(2y-1)/((2(4y-1))
= (2y-1)/(4y-1)
2. x-3)/3x-5)/3-x/6x-10
this is not clear, do you mean
(x-3/3x-5)/((3-x)(6x-10)) ?
then
(x-3)/(3x-5)*(6x-10/(3-x)
= (x-3)/(3x-5)*2(3x-5)/(-x)
= -2 , x not equal to 3 and 5/3
3. 3a+6/2a^2+7a+6
= 3(a+2)/((a+2)(2a+3)
= 3/(2a+3) x not equal to -2,-3/2
Sure! I can help you with these rational expressions. Let's go through each problem one by one.
1) 4y-2 / 8y-2
To simplify this expression, you can factor out a common factor from the numerator and the denominator:
4y - 2 = 2(2y - 1)
8y - 2 = 2(4y - 1)
Now, we can cancel out the common factor of 2:
(2(2y - 1)) / (2(4y - 1)) = (2y - 1) / (4y - 1)
This is the simplified form of the rational expression. As for the restriction, we need to find values of y for which the denominator becomes zero (since division by zero is undefined). Set the denominator equal to zero and solve for y:
4y - 1 = 0
4y = 1
y = 1/4
So, the restriction for this rational expression is y ≠ 1/4. This means that the expression is not defined when y = 1/4.
2) (x-3/3x-5) / (3-x/6x-10)
To simplify this expression, we multiply the numerator and denominator by the common denominator of the two fractions, which in this case is (3x-5)(6x-10):
[((x-3)(6x-10)) / ((3x-5)(3x-10))] * [((6x-10)(3x-5)) / ((6x-10)(3x-10))]
Simplifying the numerator and the denominator gives us:
(6x^2 - 18x - 10x + 30) / (18x^2 - 30x - 15x + 25)
(6x^2 - 28x + 30) / (18x^2 - 45x + 25)
Now, we can simplify this further by factoring both the numerator and the denominator. The numerator factors as:
6(x^2 - 4x + 5)
The denominator factors as:
(3x - 5)(6x - 5)
Canceling out the common factor of 3x - 5 gives us the simplified form:
2(x^2 - 4x + 5) / (6x - 5)
As for the restrictions, we need to find the values of x for which the denominator becomes zero. Set the denominator equal to zero and solve for x:
6x - 5 = 0
6x = 5
x = 5/6
The restriction for this rational expression is x ≠ 5/6. This means that the expression is not defined when x = 5/6.
3) (3a + 6) / (2a^2 + 7a + 6)
To simplify this expression, we can factor the numerator and the denominator:
3(a + 2) / (a + 2)(2a + 3)
Now, we can cancel out the common factor of a + 2:
3 / (2a + 3)
This is the simplified form of the rational expression. As for the restrictions, we need to find the values of a for which the denominator becomes zero. Set the denominator equal to zero and solve for a:
2a + 3 = 0
2a = -3
a = -3/2
The restriction for this rational expression is a ≠ -3/2. This means that the expression is not defined when a = -3/2.
I hope this helps you understand the rational expressions better! Let me know if you have any other questions.