Hi there! I am so confused about these questions if anyone could help that would be great.
1. Simplify. x+5/x^2+6x+5
A) 1/x+1; where x= -1***
B) 1/x+1; where x=-1,-5
C) 1/x-5; where x=5
D) x-5
2. Simplify. x^2+3x-4/x+4
A) 1/x-4; where x=4
B) x-4
C) x-1; where x=1
D) x-1; where x=-4**
3. Simplify. 3/5a*1/a^2
A) 3/5a^2; where a=0
B) 3/5a^2
C) 3/5a^3; where a=0**
D) 4/5a^2; where a=0
I have chosen my answer with **, but I still would like to have someone check it because I am confused about the "where a=?". Thank you so much!
Your answers are correct.
Be careful with brackets on a site such as this.
e.g.
in #1 you will have to type it as
(x+5)/(x^2 + 6x + 5)
and your answer is 1/(x+1), x ≠ -1
As to the x ≠ ??
the concern is the denominator,
e.g. in #1, we have x+1 as a denominator.
What happens when x = -1 ?
We would be dividing by zero, which a mathematical NONO
For every other value of x , the denominator is just a non-zero number, so we can perform the division.
e.g. sub in x = 2
in the original:
= (2+5)/(4 + 12 + 5)
= 7/21
= 1/3
now sub in x = 2 into the simplified version
= 1/(2+1)
= 1/3 , that was much easier, that's why we simplified
The same is true for #2, the denominator is (x+4)
so x ≠ =4
in #3, the denominator is simply 5a^3, so a ≠ 0
Hello! I'll be happy to help explain how to solve these questions for you.
1. To simplify the expression x + 5 / (x^2 + 6x + 5), we first factor the denominator by finding two numbers that multiply to 5 and add up to 6. These numbers are 1 and 5. So, we can rewrite the expression as x + 5 / ((x + 1)(x + 5)).
Now, we have a common factor of (x + 5) in both the numerator and denominator, so we can cancel it out. This leaves us with 1 / (x + 1).
To find the value of x that satisfies the equation 1 / (x + 1) = 1 / x + 1, we set the denominator equal to zero: x + 1 = 0. Solving this equation, we find x = -1.
Therefore, the correct answer is A) 1/x + 1, where x = -1. So, your choice for this question is correct.
2. To simplify the expression x^2 + 3x - 4 / (x + 4), we can factor the numerator by finding two numbers that multiply to -4 and add up to 3. These numbers are 4 and -1. We can rewrite the expression as (x + 4)(x - 1) / (x + 4).
Again, we have a common factor of (x + 4) in both the numerator and denominator, so we can cancel it out. This leaves us with x - 1.
To find the value of x that satisfies the equation x - 1 = x + 4, we subtract x from both sides and find that -1 = 4. Since this equation is not true for any value of x, there is no solution.
Therefore, your choice of D) x - 1, where x = -4, is incorrect. This question does not have a valid solution.
3. To simplify the expression 3 / (5a) * 1 / a^2, we can multiply the two fractions together. This results in 3 / (5a * a^2), which can be further simplified to 3 / (5a^3).
Now, to find the value of a, we need to know what a is. The "where a=?" part is asking for the value of a that satisfies the equation. Without any additional information, we cannot determine the value of a.
Therefore, your choice of C) 3 / (5a^3), where a = 0, is incorrect. The value of a needs to be specified in order to find the correct answer.
I hope this explanation helps! If you have any further questions, feel free to ask.