Question 325272
{{{(x+7)/(x^2-25)-1/(x-5)=(x^2-4)/(x^2-25)}}} Start with the given equation.



{{{(x+7)/((x+5)(x-5))-1/(x-5)=(x^2-4)/((x+5)(x-5))}}} Factor {{{x^2-25}}} to get {{{(x+5)(x-5)}}}



{{{x+7-1(x+5)=x^2-4}}} Multiply every term by the LCD {{{(x+5)(x-5)}}} to clear out the fractions.



{{{x+7-x-5=x^2-4}}} Distribute.



{{{x+7-x-5-x^2+4=0}}} Get every term to the left side.



{{{-x^2+0x+6=0}}} Rearrange the terms.



{{{x^2-6=0}}} Multiply every term by -1 to make the leading coefficient positive.



Notice that the quadratic {{{x^2-6}}} is in the form of {{{Ax^2+Bx+C}}} where {{{A=1}}}, {{{B=0}}}, and {{{C=-6}}}



Let's use the quadratic formula to solve for "x":



{{{x = (-B +- sqrt( B^2-4AC ))/(2A)}}} Start with the quadratic formula



{{{x = (-(0) +- sqrt( (0)^2-4(1)(-6) ))/(2(1))}}} Plug in  {{{A=1}}}, {{{B=0}}}, and {{{C=-6}}}



{{{x = (0 +- sqrt( 0-4(1)(-6) ))/(2(1))}}} Square {{{0}}} to get {{{0}}}. 



{{{x = (0 +- sqrt( 0--24 ))/(2(1))}}} Multiply {{{4(1)(-6)}}} to get {{{-24}}}



{{{x = (0 +- sqrt( 0+24 ))/(2(1))}}} Rewrite {{{sqrt(0--24)}}} as {{{sqrt(0+24)}}}



{{{x = (0 +- sqrt( 24 ))/(2(1))}}} Add {{{0}}} to {{{24}}} to get {{{24}}}



{{{x = (0 +- sqrt( 24 ))/(2)}}} Multiply {{{2}}} and {{{1}}} to get {{{2}}}. 



{{{x = (0 +- 2*sqrt(6))/(2)}}} Simplify the square root  (note: If you need help with simplifying square roots, check out this <a href=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>)  



{{{x = (0)/(2) +- (2*sqrt(6))/(2)}}} Break up the fraction.  



{{{x = 0 +- sqrt(6)}}} Reduce.  



{{{x = sqrt(6)}}} or {{{x = -sqrt(6)}}}  Break up the expression.  



So the solutions are {{{x = sqrt(6)}}} or {{{x = -sqrt(6)}}}