Question 171793
Simplfy:
{{{((1/(x-x^2)) - (1/(x^2+x)))/((1/(x+1))+(1/(x^2-1)))}}} Now we'll factor some of the denominators to see if we can find the LCD thus allowing us to add/subtract the fractions where so indicated.
{{{((1/x(1-x))-(1/x(x+1)))/(1/(x+1)+(1/(x-1)(x+1)))}}} The LCD for the fractions in the numerator is:{{{x(x-1)(x+1)}}} and for the denominator: {{{(x+1)(x-1)}}}, so...
{{{(((x+1)-(x-1))/(x(x-1)(x+1)))/(((x-1)+1)/((x+1)(x-1)))}}} To divide fractions, you "copy-flip-flip", that is copy the first fraction, flip the sign from divide to multiply, then flip (invert) the second fraction.
{{{(((x+1)-(1-x))/(x*cross((x-1))cross((x+1))))*((cross((x+1))cross((x-1)))/((x-1)+1))}}} Cancel the indicated factors then simplify.
{{{(((x+1)-(1-x))/x)*(1/((x-1)+1)))}}} Simplify further.
{{{(2x/x)*(1/x) = highlight(2/x)}}}