SOLUTION: solve the equation for x {{{ p=x-y/x+y}}}

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Question 156375: solve the equation for x +p=x-y%2Fx%2By
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Are you sure that the equation is +p=x-y%2Fx%2By ??


+p=x-y%2Fx%2By Start with the given equation


+px=x%5E2-y%2Bxy Multiply EVERY term by the LCD "x" to clear out the fractions.


+0=x%5E2-y%2Bxy-px Subtract px from both sides.


+0=x%5E2%2Bxy-px-y Rearrange the terms.


+0=x%5E2%2B%28y-p%29x-y Combine like terms.


x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29+ Start with the quadratic formula


x+=+%28-%28y-p%29+%2B-+sqrt%28+%28y-p%29%5E2-4%281%29%28-y%29+%29%29%2F%282%281%29%29+ Plug in a=1, b=y-p, and c=-y


x+=+%28-%28y-p%29+%2B-+sqrt%28+y%5E2-2py%2Bp%5E2-4%281%29%28-y%29+%29%29%2F%282%281%29%29+ FOIL


x+=+%28-%28y-p%29+%2B-+sqrt%28+y%5E2-2py%2Bp%5E2%2B4y+%29%29%2F%282%29+ Multiply


x+=+%28-y%2Bp+%2B-+sqrt%28+y%5E2-2py%2Bp%5E2%2B4y+%29%29%2F%282%29+ Distribute


x+=+%28-y%2Bp+%2B+sqrt%28+y%5E2-2py%2Bp%5E2%2B4y+%29%29%2F%282%29+ or x+=+%28-y%2Bp+-+sqrt%28+y%5E2-2py%2Bp%5E2%2B4y+%29%29%2F%282%29+ Break up the "plus/minus" to get two equations.


Since we cannot condense and simplify the radicand, we cannot go any further.


So the solutions are x+=+%28-y%2Bp+%2B+sqrt%28+y%5E2-2py%2Bp%5E2%2B4y+%29%29%2F%282%29+ or x+=+%28-y%2Bp+-+sqrt%28+y%5E2-2py%2Bp%5E2%2B4y+%29%29%2F%282%29+


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Or...

Is the equation +p=%28x-y%29%2F%28x%2By%29 ??


+p=%28x-y%29%2F%28x%2By%29 Start with the given equation


+p%28x%2By%29=x-y Multiply both sides by x%2By


+px%2Bpy=x-y Distribute


+px%2Bpy-x=-y Subtract x from both sides


+px-x=-y-py Subtract py from both sides


+x%28p-1%29=-y-py Factor out the GCF "x"


+x=%28-y-py%29%2F%28p-1%29 Divide both sides by p-1 to isolate "x"


So the solution is +x=%28-y-py%29%2F%28p-1%29