SOLUTION: find values of x, satisfying given conditions: y(first)=2x/(x+3); y(second)=3/(x+5) , and y(first)+y(second)=1

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Question 831255: find values of x, satisfying given conditions:
y(first)=2x/(x+3); y(second)=3/(x+5) , and y(first)+y(second)=1

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
I'm changing y(first) to y and y(second) to z just for clarity.
1.y=2x%2F%28x%2B3%29
2.z=3%2F%28x%2B5%29
3.y%2Bz=1
From eq. 3, substitute using eq. 1 and eq. 2,
2x%2F%28x%2B3%29%2B3%2F%28x%2B5%29=1
2x%28x%2B5%29%2B3%28x%2B3%29=%28x%2B3%29%28x%2B5%29
2x%5E2%2B10x%2B3x%2B9=x%5E2%2B8x%2B15
2x%5E2%2B13x%2B9=x%5E2%2B8x%2B15
x%5E2%2B5x-6=0
%28x%2B6%29%28x-1%29=0
To possible solutions:
x%2B6=0
x=-6
Check the original equation:
y=2%28-6%29%2F%28-6%2B3%29=-12%2F-3=4
z=3%2F%28-6%2B5%29=3%2F%28-1%29=-3
y%2Bz=1
True
.
.
.
x-1=0
x=1
Check the original equation:
y=2%281%29%2F%281%2B3%29=2%2F4=1%2F2
z=3%2F%281%2B5%29=3%2F6=1%2F2
y%2Bz=1
True
(x,y,z)=(-6,4,-3)
(x,y,z)=(1,1/2,1/2)