<PRE><B>Question 176562</B>
Solve {{{1/x}}} + {{{1/(x+5)}}} = {{{3/4}}}
mult eq by common denominator, 4x(x+5)
4x(x+5)*{{{1/x}}} + 4x(x+5)*{{{1/(x+5)}}} = 4x(x+5)*{{{3/4}}}
cancel out the denominators
4(x+5) + 4x = 3x(x+5)
;
4x + 20 + 4x = 3x^2 + 15x
:
8x + 20  = 3x^2 + 15x
;
0 = 3x^2 + 15x - 8x - 20
;
3x^2 + 7x - 20 = 0; a quadratic eq
factor this to
(3x - 5)(x + 4) = 0
two solutions
3x = 5
;
x = {{{5/3}}}
and
x = -4
:
check both solutions in original eq</PRE>