SOLUTION: Write the given expression as a single quotient in which only positive exponents and/or radicals appear. [(8x + 1)^(1/3)]/[3(x - 2)^(1/2)]^(1/3) + [(x - 2)^(1/3)]/[24(8x + 1)^

Algebra ->  Expressions -> SOLUTION: Write the given expression as a single quotient in which only positive exponents and/or radicals appear. [(8x + 1)^(1/3)]/[3(x - 2)^(1/2)]^(1/3) + [(x - 2)^(1/3)]/[24(8x + 1)^      Log On


   



Question 1208445: Write the given expression as a single quotient in which only positive exponents and/or radicals appear.

[(8x + 1)^(1/3)]/[3(x - 2)^(1/2)]^(1/3) + [(x - 2)^(1/3)]/[24(8x + 1)^(1/2)]^(1/3)

Note: x does not equal 2; x does not equal -1/8

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
If x%3C%3E2 and X%3C%3E-1%2F8 then x-2%3C%3E0 and 8x%2B1%3C%3E0 .
In that case, multiplying numerator and denominator of a fraction times those expressions results in a fraction that is equivalent for all considered values of x .
%288x+%2B+1%29%5E%221%2F3%22%2F%28%283%28x+-+2%29%29%5E%221%2F2%22%29%5E%221%2F3%22%29 %22%2B%22 %28%28x+-+2%29%5E%221%2F3%22%29%2F%28%2824%288x+%2B+1%29%29%5E%221%2F2%22%29%5E%221%2F3%22%22=%22 %288x+%2B+1%29%5E%221%2F3%22%2F%28%283%5E%221%2F3%22%29%28x+-+2%29%5E%221%2F6%22%29%29 %22%2B%22 %22=%22 %288x+%2B+1%29%5E%221%2F3%22%2F%28%283%5E%221%2F3%22%29%28x+-+2%29%5E%221%2F6%22%29%29 %22%2B%22

%22=%22 %22%2B%22

%22=%22 %282%288x+%2B+1%29%5E%221%2F3%2B1%2F6%22%29%2F%0D%0A%282%288x%5E2-15x-2%29%5E%221%2F6%22%29 %22%2B%22 %28%28x+-+2%29%5E%221%2F3%2B1%2F6%22%29%2F%282%288x%5E2-15x-2%29%5E%221%2F6%22%29%22=%22 %282%288x+%2B+1%29%5E%221%2F2%22%29%2F%0D%0A%282%288x%5E2-15x-2%29%5E%221%2F6%22%29 %22%2B%22 %28%28x+-+2%29%5E%221%2F2%22%29%2F%282%288x%5E2-15x-2%29%5E%221%2F6%22%29%22=%22

%22=%22 %282sqrt%288x+%2B+1%29%2Bsqrt%28x+-+2%29%29%2F%0D%0A%282root%286%2C%288x%5E2-15x-2%29%29%29