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

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

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) (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.
:
=
:
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
:
:
- =
:
Factor out 3 in the 1st denominator:
- =
:
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
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