Question 82454
#1 Perform the indicated operation and simplify:
2x/x^2-4 +5/2-x -1/2+x
{{{2x/((x^2-4)) +  5/((2-x)) - 1/((2+x))}}}
:
4{{{2x/((x-2)(x+2)) +  5/((2-x)) - 1/((2+x))}}}; Factored x^2 - 4
:
{{{2x/((x-2)(x+2)) +  5/(-1(x-2)) - 1/((x+2))}}}; converted 2-x to x-2 with -1
:
{{{2x/((x-2)(x+2)) -  5/((x-2)) - 1/((x+2))}}}; -1 changes the sign
:
{{{(2x - 5(x+2) - 1(x-2))/((x-2)(x+2))}}}; put all over one denominator
:
{{{(2x - 5x - 10 - x + 2)/((x-2)(x+2))}}} = {{{(- 4x - 8)/((x-2)(x+2))}}} = {{{(-4(x + 2))/((x-2)(x+2))}}} = {{{-4/((x-2))}}}
:
:
#2 Solve
{{{2 + (7/x) = 4/x^2}}}
:
{{{2x^2 + 7x = 4}}}; multiplied equation by x^2
:
{{{2x^2 + 7x - 4}}} = 0
:
(2x-1)(x+4) = 0
:
2x = +1
x = +1/2
and
x = -4
:
Check both solutions by substituting in original equation