Question 62876
This one is much more do-able!!!
{{{6/(x-2)+7/(x^2-4)=(x+3)/(x+2)}}}  First factor
{{{6/(x-2)+7/((x-2)(x+2))=(x+3)/(x+2)}}}
The LCD is (x-2)(x+2), the restricted values are x not= =\-2 (No 0 in denominator.)  Multiply everything byt the LCD and the denominators melt away.
{{{6(x-2)(x+2)/(x-2)+7(x-2)(x+2)/((x-2)(x+2))=(x+3)(x-2)(x+2)/(x+2)}}}
{{{6*cross((x-2))(x+2)/cross((x-2))+7*cross((x-2)(x+2))/cross((x-2)(x+2))=(x+3)(x-2)*cross((x+2))/cross((x+2))}}}
{{{6(x+2)+7=(x+3)(x-2)}}}
{{{6x+12+7=x^2-2x+3x-6}}}
{{{6x+19=x^2+x-6}}}
{{{6x-6x+19-19=x^2+x-6x-6-19}}}
{{{0=x^2-5x-25}}}
The Quadratic formula is{{{highlight(x=(-b+-sqrt(b^2-4ac))/2a)}}}
a=1, b=-5, and c=-25
{{{x=(-(-5)+-sqrt((-5)^2-4(1)(-25)))/(2(1))}}}
{{{x=(5+-sqrt(25+100))/2}}}
{{{x=(5+-sqrt(125))/2}}}
{{{x=(5-sqrt(25)*sqrt(5))/2}}}  and {{{x=(5+sqrt(25)*sqrt(5))/2}}}
{{{x=(5-5*sqrt(5))/2}}} and {{{x=(5+5*sqrt(5))/2}}}
x~~-3.090169944  and x~~8.090169944
Check the answers in your calculator in the original equation and you'll see they both work.
Happy Calculating!!!