Question 762090
Problem 1:

{{{4/(x+6)+3/(x-6)=1}}} Multiplying both sides by (x+6)*(x-6)

{{{4*(x-6) + 3*(x+6) = (x+6)*(x-6)}}}

{{{4*x - 24 + 3*x + 18 = x^2 - 36}}}

{{{x^2 - 7*x - 30 = 0}}} ---> Standard quadratic equation

Let us solve it by factoring.

{{{x^2 - 10*x + 3*x - 30 = 0}}} Rewrite -7x as -10x + 3x

{{{x*(x - 10) + 3*(x - 10) = 0}}} Take out common factor of x-10

{{{(x + 3)*(x - 10) = 0}}}

Two solutions of the equation are x + 3 = 0 or x - 10 = 0

So roots of the equation are {{{highlight(x = -3)}}} and {{{highlight(x = +10)}}}

Problem 2

{{{1/(x+6) + 1/(x+5) = 1}}}

Multiply both sides by (x+6)*(x+5)

{{{x + 5 + x + 6 = (x+5)*(x+6)}}}

{{{2*x + 11 = x^2 + 11*x + 30}}}

{{{x^2 + 9*x + 19 = 0}}}

Solve using quadratic formula, as shown below. You get the 2 roots as 

{{{highlight(x = -3.382)}}} or {{{highlight(x = -5.618)}}}

*[invoke quadratic "x", 1, 9, 19 ]


Problem 3:

x^2 = 11

{{{x = sqrt(11)}}} or {{{x = -sqrt(11)}}}

:)