1.Simplify the difference.
n^2 - lOn+24 9 /
n^2 - 13n + 42 — 7
A. n-13/n-7 <<<
B. n-4/n-7
C. n-13
2.Simplify the complex fraction.
y-1/y^2+y-6/y-6/y+3
A.(y-1)(y-6)/(y+3)^2(y-2)
B. y-1/(y-6)(y-2)
C.(y-1)(y-6)/(y+3)(y-2)<<<
3.Find the least common multiple of x^3-x^2+x-1 and x^2-1 . Write the answer in factored form.
A. (x+1)^2(x-1)
B. (x+1)(x-1)(x^2+1)
C. (x^3-x^2+x-1)(x^2-1)<<<
4.Simplify the rational expression. State any restrictions on the variable.
t^2-4t-32/t-8
A. t-4;t=-8 <<<
B. t+4;t=8
C.-t-4;t=8
CHECK MY ANSWERS PLEASE!
Sure, let's go through each question and find the correct answers.
1. To simplify the difference (n^2 - 10n + 24 - 9) / (n^2 - 13n + 42 - 7), we can simplify the numerator and denominator separately.
The numerator simplifies to n^2 - 10n + 15 by combining like terms (-9 + 24 = 15).
The denominator simplifies to n^2 - 13n + 35 by combining like terms (42 - 7 = 35).
Now, we have (n^2 - 10n + 15) / (n^2 - 13n + 35). To simplify this further, we need to factor the numerator and denominator.
The numerator can be factored as (n - 5)(n - 3).
The denominator can be factored as (n - 5)(n - 7).
Now we can cancel out the common factor (n - 5) from the numerator and denominator, and we're left with (n - 3) / (n - 7).
Therefore, the correct answer is A. n - 3 / n - 7.
2. To simplify the complex fraction (y - 1) / (y^2 + y - 6) divided by (y - 6) / (y + 3), we can simplify the numerator and the denominator separately.
Simplifying the numerator, (y - 1) / (y^2 + y - 6), we can factor the denominator as (y + 3)(y - 2) and we're left with (y - 1) / ((y + 3)(y - 2)).
Simplifying the denominator, (y - 6) / (y + 3), we can cancel out the common factor of (y + 3), and we're left with (y - 6).
Now we can simply divide (y - 1) / ((y + 3)(y - 2)) by (y - 6).
To divide fractions, we keep the first fraction as it is and multiply it by the reciprocal of the second fraction. So we have (y - 1) / ((y + 3)(y - 2)) × (y - 6).
Multiplying the numerators (y - 1) × (y - 6) and the denominators ((y + 3)(y - 2)), we get (y - 1)(y - 6) / ((y + 3)(y - 2)).
Therefore, the correct answer is C. (y - 1)(y - 6) / (y + 3)(y - 2).
3. To find the least common multiple (LCM) of x^3 - x^2 + x - 1 and x^2 - 1, we need to factor both expressions completely.
The expression x^3 - x^2 + x - 1 is already fully factored.
The expression x^2 - 1 can be factored as (x + 1)(x - 1).
Now, we can take the product of all the factors, considering the highest powers for each variable. So the LCM would be (x + 1)(x - 1)(x^3 - x^2 + x - 1).
Therefore, the correct answer is C. (x^3 - x^2 + x - 1)(x^2 - 1).
4. To simplify the rational expression (t^2 - 4t - 32) / (t - 8) and state any restrictions on the variable, we can factor the numerator and the denominator.
The numerator can be factored as (t - 8)(t + 4).
The denominator is already factored.
Now, we can cancel out the common factor (t - 8) from the numerator and denominator, and we're left with (t + 4).
There are no restrictions on the variable t since we can simplify the expression for any value of t except t = 8.
Therefore, the correct answer is B. t + 4; t ≠ 8.
Hope this helps!