SOLUTION: Hello, I need some help with a couple of problems that are giving me a hard time. Any and all help will be appreciated. They are: 1. Divide: x^2 - 9x +8/2x - 4 / x^2 - 1/

Algebra ->  Radicals -> SOLUTION: Hello, I need some help with a couple of problems that are giving me a hard time. Any and all help will be appreciated. They are: 1. Divide: x^2 - 9x +8/2x - 4 / x^2 - 1/      Log On


   

Question 201757: Hello,
I need some help with a couple of problems that are giving me a hard time. Any and all help will be appreciated. They are:
1. Divide: x^2 - 9x +8/2x - 4 / x^2 - 1/2x + 2
2. Perform the indicated operations: 4sqrt[50] + sqrt[32] - sqrt[18]
Again, any and all help will be appreciated.
Thank you in advance for your help.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
# 1


%28%28x%5E2-9x%2B8%29%2F%282x-4%29%29%2F%28%28x%5E2-1%29%2F%282x%2B2%29%29 Start with the given expression.


%28%28x%5E2-9x%2B8%29%2F%282x-4%29%29%28%282x%2B2%29%2F%28x%5E2-1%29%29 Multiply the first fraction %28x%5E2-9x%2B8%29%2F%282x-4%29 by the reciprocal of the second fraction %28x%5E2-1%29%2F%282x%2B2%29.


%28%28%28x-1%29%2A%28x-8%29%29%2F%282x-4%29%29%28%282x%2B2%29%2F%28x%5E2-1%29%29 Factor x%5E2-9x%2B8 to get %28x-1%29%2A%28x-8%29.


%28%28%28x-1%29%2A%28x-8%29%29%2F%282%28x-2%29%29%29%28%282x%2B2%29%2F%28x%5E2-1%29%29 Factor 2x-4 to get 2%28x-2%29.


%28%28%28x-1%29%2A%28x-8%29%29%2F%282%28x-2%29%29%29%28%282%28x%2B1%29%29%2F%28x%5E2-1%29%29 Factor 2x%2B2 to get 2%28x%2B1%29.


Factor x%5E2-1 to get %28x-1%29%2A%28x%2B1%29.


%282%28x-1%29%28x-8%29%28x%2B1%29%29%2F%282%28x-2%29%28x-1%29%2A%28x%2B1%29%29 Combine the fractions.


Highlight the common terms.


Cancel out the common terms.


%28x-8%29%2F%28x-2%29 Simplify.


So %28%28x%5E2-9x%2B8%29%2F%282x-4%29%29%2F%28%28x%5E2-1%29%2F%282x%2B2%29%29 simplifies to %28x-8%29%2F%28x-2%29.


In other words,




# 2



4%2Asqrt%2850%29%2Bsqrt%2832%29-sqrt%2818%29 Start with the given expression


4%2A5%2Asqrt%282%29%2Bsqrt%2832%29-sqrt%2818%29 Simplify sqrt%2850%29 to get 5%2Asqrt%282%29. Note: If you need help with simplifying square roots, check out this solver.


4%2A5%2Asqrt%282%29%2B4%2Asqrt%282%29-sqrt%2818%29 Simplify sqrt%2832%29 to get 4%2Asqrt%282%29.


4%2A5%2Asqrt%282%29%2B4%2Asqrt%282%29-3%2Asqrt%282%29 Simplify sqrt%2818%29 to get 3%2Asqrt%282%29.


20%2Asqrt%282%29%2B4%2Asqrt%282%29-3%2Asqrt%282%29 Multiply 4 and 5 to get 20.


%2820%2B4-3%29sqrt%282%29 Factor out the GCF sqrt%282%29


21%2Asqrt%282%29 Combine like terms.


So 4%2Asqrt%2850%29%2Bsqrt%2832%29-sqrt%2818%29 simplifies to 21%2Asqrt%282%29.


In other words, 4%2Asqrt%2850%29%2Bsqrt%2832%29-sqrt%2818%29=21%2Asqrt%282%29