Question

solve the equation 1/x-7+1/x+7=-5/x^2-49

Answer 1

\[\frac{ 1 }{ x-7 }+\frac{ 1 }{ x+7 }=\frac{ -5 }{ x^2-49 }\]
multiply both sides by \[x^2-49 \] and solve for x

Answer 2

1/x-7+1/x+7=-5/x^2-49
take LCM OF LHS equation.
(x+7)+ (x-7)/(x-7) (x+7)=-5/x^2-49
by making use of identity (a+b)(a-b) = a2-b2
((x+7)+ (x-7) )/ (x2-72)=-5/x^2-49
((x+7)+ (x-7) )/ (x2-49)=-5/x^2-49
multiply both side of the equation by (x^2-49 )
((x+7)+ (x-7) )=-5
x+7+x-7 = -5
2x = -5
x = -5/2