<PRE><B>Question 75319</B>
42. x/9-8/x=1/9
{{{x/9 - 8/x}}} = {{{1/9}}}
:
We want to get rid of the denominators, 9x is a common denominator so multiply
each term in the equation by 9x, this will cancel out the denominators and
give you:
x*x - 9(8) = x
x^2 - 72 = x
:
Subtract x from both sides and you have a quadratic equation:
x^2 - x - 72 = 0
Easily factored to:
(x-9)(x+8) = 0
:
x =+9 and x = -8
:
Substitute both of these in the original equation to check our solutions
x = 9
{{{9/9 - 8/9}}} = {{{1/9}}}
x = -8
{{{-8/9 - (8/-8)}}} = {{{1/9)}}}
{{{-8/9 + (8/8)}}} = {{{1/9)}}}
{{{-8/9 + 1}}} = {{{1/9)}}}
:
:
43. (x+42)/x = x 
{{{((x+42))/x}}} = x
:
Multiply equation by x, gets rid of the denominator and you have;
x + 42 = x^2
0 = x^2 -x - 42; another easily factored quadratic equation:
(x-7)(x+6) = 0
x = +7 and x = -6
:
You can check the solutions by substituting both values in the original eq</PRE>