Question 184426
I think you have the right idea, but here it is step-by-step:
:
Solve {{{(x/6)+((x+4)/2)=(2/(x+5))}}}
the common denominator would be 6(x+5), multiply thru by that:
6(x+5)*{{{x/6}}}+ 6(x+5)*{{{(x+4)/2}}} = 6(x+5)*{{{2/(x+5)}}}
:
Cancel out the denominators and you have:
x(x+5) + 3(x+5)(x+4) = 6(2)
:
x^2 + 5x + 3(x^2+ 9x + 20) = 12
:
x^2 + 5x + 3x^2 + 27x + 60 = 12
Combine like terms
x^2 + 3x^2 + 5x + 27x + 60 - 12 = 0
:
4x^2 + 32x + 48 = 0
simplify divide by 4
x^2 + 8x + 12 = 0
Factors to
(x+6)(x+2) = 0
x = -6
x = -2
:
:
Check both solution in original equation
x=-6
{{{((-6)/6)+((-6+4)/2)=(2/(-6+5))}}}
{{{((-6)/6)+((-2)/2)=(2/(-1))}}}
-1 - 1 = -2
:
you can check x=-2