SOLUTION: make x the subject of the formula 1. x/x+a - a/x+b = 1 2. x^2/a^2 + y^2/b^2 = 1 3. a(a^2- x) = b(b^2 - x) 4. a/a-x = b/b+x

Algebra ->  Functions -> SOLUTION: make x the subject of the formula 1. x/x+a - a/x+b = 1 2. x^2/a^2 + y^2/b^2 = 1 3. a(a^2- x) = b(b^2 - x) 4. a/a-x = b/b+x      Log On


   

Question 1101236: make x the subject of the formula
1. x/x+a - a/x+b = 1
2. x^2/a^2 + y^2/b^2 = 1
3. a(a^2- x) = b(b^2 - x)
4. a/a-x = b/b+x
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
make x the subject of the formula
1. x%2F%28x%2Ba%29+-+a%2F%28x%2Bb%29+=+1
multiply by (x+a)(x+b), cancel the denominators
x(x+b) - a(x+a) = (x+a)(x+b)
distribute, FOIL
x^2 + bx - ax - a^2 = x^2 + bx + ax + ab
combine like terms
x^2 - x^2 - ax - ax = a^2 + bx - bx + ab
-2ax = a^2 + ab
x+=+%28a%5E2%2Bab%29%2F%28-2a%29
factor out a
x+=+%28a%28a%2Bb%29%29%2F%28-2a%29
Cancel a
x+=+-%28a%2Bb%29%2F2
:
2. x%5E2%2Fa%5E2+%2B+y%5E2%2Fb%5E2+=+1
multiply equation by a^2b^2
b%5E2x%5E2+%2B+a%5E2y%5E2+=+a%5E2b%5E2
b%5E2x%5E2+=+a%5E2b%5E2+-+a%5E2y%5E2
b%5E2x%5E2+=+a%5E2%28b%5E2-y%5E2%29
x%5E2+=+%28a%5E2%28b%5E2-y%5E2%29%29%2Fb%5E2
x+=+sqrt%28%28a%5E2%28b%5E2-y%5E2%29%29%2Fb%5E2%29
extract the squares
x+=+%28a%2Fb%29sqrt%28b%5E2-y%5E2%29
:
Will finish later today, these are time consuming.
:
3. a%28a%5E2-+x%29+=+b%28b%5E2+-+x%29
a^3 - ax = b^3 - bx
bx - ax = b^3 - a^3
x(b-a) = b^3 - a^3
x = %28b%5E3-a%5E3%29%2F%28b-a%29
:
4. a%2F%28a-x%29+=+b%2F%28b%2Bx%29
cross multiply
a(b+x) = b(a-x)
ab + ax = ab - bx
bx + ax = ab - ab
bx + ax = 0
x(b + a) = 0
x = 0%2F%28%28b%2Ba%29%29
x = 0