SOLUTION: Factor the expression. 25x^2(4+x^2)^-3/2 + 6x(4+x^2)^-1/2 I factored by grouping and got x(1+4x^2)^-3/2[25x+6(1+4x^2)^-2] but I don't know where to go from there. Please help!

Algebra ->  Expressions -> SOLUTION: Factor the expression. 25x^2(4+x^2)^-3/2 + 6x(4+x^2)^-1/2 I factored by grouping and got x(1+4x^2)^-3/2[25x+6(1+4x^2)^-2] but I don't know where to go from there. Please help!      Log On


   



Question 836632: Factor the expression.
25x^2(4+x^2)^-3/2 + 6x(4+x^2)^-1/2
I factored by grouping and got x(1+4x^2)^-3/2[25x+6(1+4x^2)^-2] but I don't know where to go from there. Please help!

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
25x%5E2%284%2Bx%5E2%29%5E%28-3%2F2%29+%2B+6x%284%2Bx%5E2%29%5E%28-1%2F2%29+
since 1%2F%28sqrt%284%2Bx%5E2%29%5E3%29=1%2F%28%284%2Bx%5E2%29sqrt%284%2Bx%5E2%29%29+ and %284%2Bx%5E2%29%5E%28-1%2F2%29=1%2Fsqrt%284%2Bx%5E2%29+, we have

25x%5E2%2F%28%284%2Bx%5E2%29sqrt%284%2Bx%5E2%29%29+%2B+6x%2Fsqrt%284%2Bx%5E2%29



%2825x%5E2+%2B+6x%284%2Bx%5E2%29%29%2F%28%284%2Bx%5E2%29sqrt%284%2Bx%5E2%29%29

%2825x%5E2+%2B+24x%2B6x%5E3%29%2F%28%284%2Bx%5E2%29sqrt%284%2Bx%5E2%29%29

x%2825x+%2B+24%2B6x%5E2%29+%2F%28%284%2Bx%5E2%29sqrt%284%2Bx%5E2%29%29....replace %2825x+%2B+24%2B6x%5E2%29 with %282x%2B3%29%283x%2B8%29

+%28x%282x%2B3%29%283x%2B8%29%29%2F%28%284%2Bx%5E2%29sqrt%284%2Bx%5E2%29%29+