SOLUTION: Dear Sir/Madam, I am confronted with the following problem: "Simplify the expression. (3x + 1)^6 * (1/2) * (2x - 5)^(-1/2) * (2) + (2x

SOLUTION: Dear Sir/Madam, I am confronted with the following problem: "Simplify the expression. (3x + 1)^6 * (1/2) * (2x - 5)^(-1/2) * (2) + (2x - 5)^(1/2) * (6) * (3x + 1)^5 * (3)."

Question 6608: Dear Sir/Madam,
I am confronted with the following problem:
"Simplify the expression.
(3x + 1)^6 * (1/2) * (2x - 5)^(-1/2) * (2) + (2x - 5)^(1/2) * (6) * (3x + 1)^5 * (3)."
I did the following:
[(3x + 1)^6 / (2x - 5)^(1/2)] + 18(2x - 5)^(1/2) * (3x + 1)^5
but now I don't know how to proceed. I tried setting (2x - 5)^(1/2) as a common denominator and actually doing the addition, but I couldn't get it to work. Can you help me out please?
Thanks in advance.
Regards,
-Mike
Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
This looks like a factoring problem that came out of a Calculus problem. The first step that you did is okay, but I prefer to just factor the problem outright. Take out the common factors from the two terms here. The common factor is always the factor raised to the lowest power. In this case, the common factor to be taken out is . Remember also that when you take out a common factor, you subtract exponents to determine what is "left over".

Notice that in the first term the 1/2 and the 2 divide out. What is left in the first position is (3x+1), and in the second position, you have left or and also a which is .

Also:

Note: You might want to check me out on this one! That was a lot of heavy duty factoring and equation boxes. Did you have an answer to check?

R^2 at SCC
RELATED QUESTIONS
Dear Sir/Madam, I am confronted with the following problem: "Evaluate {{{ log( 5,... (answered by ichudov)

Dear Sir/Madam, I am confronted with the following problem: "Solve the equation. (answered by prince_abubu)

Dear Sir/Madam, I am confronted with the following problem: "Find the equation of (answered by rapaljer,Mike)

Dear Sir/Madam, I am confronted with the following problem: "Solve the... (answered by rapaljer)

Dear Sir/Madam, I am confronted with the following problem: "Find a polar equation... (answered by ichudov)

Dear Sir/Madam, I am confronted with the following problem: "T varies directly as... (answered by longjonsilver)

Dear Sir/Madam, I am confronted with the following problem: "The expression... (answered by longjonsilver)

Dear Sir/Madam, I am confronted with the following problem: "Where does the graph... (answered by ichudov,dval9159)

Dear Sir/Madam, I'm struggling with absolute value equation of this type:... (answered by josgarithmetic)