SOLUTION: Solve each equation. a+4/2 = a+4/a and 4w-1/3w+6 - w-1/3 = w-1/w+2

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Solve each equation. a+4/2 = a+4/a and 4w-1/3w+6 - w-1/3 = w-1/w+2      Log On


   

Question 77385: Solve each equation.
a+4/2 = a+4/a
and
4w-1/3w+6 - w-1/3 = w-1/w+2
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Solve each equation.
:
I have to assume what you mean here, a few brackets would help a lot.
:
%28%28a%2B4%29%29%2F2 = %28%28a%2B4%29%29%2Fa
:
Cross multiply and you have:
a(a+4) = 2(a+4)
a^2 + 4a = 2a + 8
a^2 + 4a - 2a - 8 = 0
a^2 + 2a - 8 = 0; a quadratic equation
Factors to:
(a+4)(a-2) = 0
a = -4
and
a = +2
:
Check both solutions in the original equation
:
:
%28%284w-1%29%29%2F%28%283w%2B6%29%29 - %28%28w-1%29%29%2F3 = %28%28w-1%29%29%2F%28%28w%2B2%29%29
:
Factor out 3 in the 1st denominator:
%28%284w-1%29%29%2F%283%28w%2B2%29%29 - %28%28w-1%29%29%2F3 = %28%28w-1%29%29%2F%28%28w%2B2%29%29
:
Multiply thru by the common denominator, 3(w+2), you then have
(4w-1) - ((w-1)(w+2)) = 3(w-1)
:
FOIL (w-1)(w+2) and what's inside the brackets:
(4w-1) - (w^2 + w - 2) = 3w - 3
:
Remove the brackets:
4w - 1 - w^2 - w + 2 = 3w - 3
-w^2 + 3w + 1 = 3w - 3
-w^2 + 3w - 3w + 1 + 3 = 0
-w^2 + 4 = 0
w^2 - 4 = 0; Multiplied equation by -1
w^2 = +4
w = +2
:
Check the solution, substitute 2 for w in the original equation