Can someone check my algebra answers and help me with the problems I don't understand?
1. n^2-n-20/2n^2 times n^2+5n/n^2-25
answer: n+4/2n
2. (2x-6/21)/(5x-15/12)
answer: 8/35
3. 5x-3/6 - x+3/6
answer: 2x/3-1
4. 5x/26 - 2x/13
answer: 1x/26
5. 3x^2/9x^5
answer: 1/3x^3
6. (x^2+2x-15/4x^2)/(x^2-25/2x-10...
answer: I'm not to sure but i think its x-3/2x^2
7. x+2/x/x-2/3x
answer: 3(x+2)/x-2
8. What values for x must be excluded in the following fraction?
9/x-8
answer: 8
9. x-13/x^2-x-12 + 3x-3/x^2-x-12
answer: 4/x+3
Sometimes it helps to use parentheses when typing these kinds of problems online. From what I can determine, these answers look correct, except for #3. (For #4, you can just state the answer as x/26.)
Here's #3 worked out:
(5x-3)/6 - (x+3)/6 =
(5x-3-x-3)/6 =
(4x-6)/6 =
2(2x-3)/6 =
(2x-3)/3
I hope this will help.
Well, it looks like you're doing a great job with your algebra problems! As for #3, you're really close, but let me give it a little twist:
(5x - 3) / 6 - (x + 3) / 6 =
(5x - x - 3 - 3) / 6 =
(4x - 6) / 6 =
2(2x - 3) / 3 =
2(2x - 3) / 2(3) =
(2x - 3) / 3
So, the answer is actually (2x - 3) / 3. Keep up the good work!
Here's a step-by-step explanation for each of the problems:
1. (n^2 - n - 20) / (2n^2) * (n^2 + 5n) / (n^2 - 25)
Factor the numerator of the first fraction: (n - 5)(n + 4)
Factor the denominator of the second fraction: (n - 5)(n + 5)
Cancel out common factors and simplify: (n + 4) / (2n)
2. ((2x - 6) / 21) / ((5x - 15) / 12)
Invert the second fraction and multiply: (2x - 6) / 21 * 12 / (5x - 15)
Simplify the numerator and denominator: (2x - 6) * 12 / (21 * (5x - 15))
Simplify further: (2x - 6) * 4 / (7 * (5x - 15))
Distribute and cancel out common factors: (8x - 24) / (35x - 105)
Simplify: 8(x - 3) / 35(x - 3)
Cancel out common factors: 8/35
3. (5x - 3) / 6 - (x + 3) / 6
Combine the fractions over a common denominator: (5x - 3 - x - 3) / 6
Simplify: (4x - 6) / 6
Factor out a common factor: 2(2x - 3) / 6
Simplify further: (2x - 3) / 3
4. 5x / 26 - 2x / 13
The denominators are already the same, so subtract the numerators: (5x - 2x) / 26
Simplify: 3x / 26
The numerator and denominator do not have any common factors, so this is the final answer.
5. (3x^2) / (9x^5)
Simplify the numerator and denominator: 3 / (3x^3 * x^2)
Divide the numerator and denominator by 3: 1 / (x^3 * x^2)
Combine the exponents: 1 / (x^(3+2))
Simplify: 1 / x^5
6. ((x^2 + 2x - 15) / 4x^2) / ((x^2 - 25) / (2x - 10))
Invert the second fraction and multiply: (x^2 + 2x - 15) / 4x^2 * (2x - 10) / (x^2 - 25)
Factor the numerator and denominator of the first fraction: (x - 3)(x + 5) / (2x)^2 * (2x - 10) / (x - 5)(x + 5)
Cancel out common factors: (x - 3) / 4x * 2 / (x - 5)
Simplify: (x - 3)(2) / 4x(x - 5)
Multiply across: 2(x - 3) / 4x(x - 5)
Simplify: (x - 3) / 2x(x - 5)
Rewriting the answer as (x - 3) / (2x(x - 5)) would be more accurate.
7. (x + 2) / x / (x - 2) / (3x)
Invert the second fraction and multiply: (x + 2) / x * (3x) / (x - 2)
Combine the numerators and denominators: (x + 2)(3x) / x(x - 2)
Distribute and simplify: 3x^2 + 6x / x^2 - 2x
Factor out a common factor: 3x(x + 2) / x(x - 2)
Cancel out common factors: 3(x + 2) / (x - 2)
Simplify further: 3(x + 2) / (x - 2)
8. The fraction 9/(x - 8) is undefined when the denominator is equal to zero, so x - 8 = 0
Solve for x: x = 8
Therefore, the value 8 must be excluded from the allowed values of x.
9. (x - 13) / (x^2 - x - 12) + (3x - 3) / (x^2 - x - 12)
Combine the fractions over a common denominator: (x - 13 + 3x - 3) / (x^2 - x - 12)
Simplify the numerator: 4x - 16
Factor the denominator: (x - 4)(x + 3)
Cancel out common factors: (4x - 16) / (x - 4)(x + 3)
We don't have enough information to simplify further.
To check your algebraic answers, you can follow these steps:
1. For problem #1:
- Simplify the expression:
(n^2 - n - 20) / (2n^2) * (n^2 + 5n) / (n^2 - 25)
- Factorize the numerator and denominator:
[(n - 5)(n + 4)] / (2n^2) * [n(n + 5)] / [(n - 5)(n + 5)]
- Simplify the expression:
[n(n - 5)(n + 4)(n + 5)] / [2n^2(n - 5)(n + 5)]
- Cancel out common terms:
[n(n + 4)] / (2n^2)
- Simplify further:
(n + 4) / (2n)
2. For problem #2:
- Simplify the expression:
(2x - 6) / 21 / (5x - 15) / 12
- Invert the divisor and multiply:
(2x - 6) / 21 * 12 / (5x - 15)
- Cancel out common factors:
(2(x - 3)) / (7(x - 3))
- Simplify further:
2/7
3. For problem #6:
- Simplify the expression:
(x^2 + 2x - 15) / (4x^2) / (x^2 - 25) / (2x - 10)
- Invert the divisor and multiply:
(x^2 + 2x - 15) / (4x^2) * (2x - 10) / (x^2 - 25)
- Factorize the numerator and denominator:
[(x - 3)(x + 5)] / (2x)(x)(x + 5)(x - 5) * 2(x - 5) / [(x + 5)(x - 5)]
- Cancel out common factors:
[(x - 3)] / [(2x)(x)]
For the other problems, the answers seem correct or require no further explanation.
If you have any specific problems or concepts you don't understand, please provide more details, and I would be happy to explain them to you.