Question 156375
Are you sure that the equation is {{{ p=x-y/x+y}}} ??



{{{ p=x-y/x+y}}} Start with the given equation



{{{ px=x^2-y+xy}}} Multiply <b>EVERY</b> term by the LCD "x" to clear out the fractions.



{{{ 0=x^2-y+xy-px}}} Subtract {{{px}}} from both sides.



{{{ 0=x^2+xy-px-y}}} Rearrange the terms.



{{{ 0=x^2+(y-p)x-y}}} Combine like terms.



{{{x = (-b +- sqrt( b^2-4ac ))/(2a) }}} Start with the quadratic formula



{{{x = (-(y-p) +- sqrt( (y-p)^2-4(1)(-y) ))/(2(1)) }}} Plug in {{{a=1}}}, {{{b=y-p}}}, and {{{c=-y}}}



{{{x = (-(y-p) +- sqrt( y^2-2py+p^2-4(1)(-y) ))/(2(1)) }}} FOIL



{{{x = (-(y-p) +- sqrt( y^2-2py+p^2+4y ))/(2) }}} Multiply



{{{x = (-y+p +- sqrt( y^2-2py+p^2+4y ))/(2) }}} Distribute



{{{x = (-y+p + sqrt( y^2-2py+p^2+4y ))/(2) }}} or {{{x = (-y+p - sqrt( y^2-2py+p^2+4y ))/(2) }}} 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 = (-y+p + sqrt( y^2-2py+p^2+4y ))/(2) }}} or {{{x = (-y+p - sqrt( y^2-2py+p^2+4y ))/(2) }}}



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Or...


Is the equation {{{ p=(x-y)/(x+y)}}} ??



{{{ p=(x-y)/(x+y)}}} Start with the given equation



{{{ p(x+y)=x-y}}} Multiply both sides by {{{x+y}}}



{{{ px+py=x-y}}} Distribute



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



{{{ px-x=-y-py}}} Subtract {{{py}}} from both sides



{{{ x(p-1)=-y-py}}} Factor out the GCF "x"



{{{ x=(-y-py)/(p-1)}}} Divide both sides by {{{p-1}}} to isolate "x"



So the solution is {{{ x=(-y-py)/(p-1)}}}