Question 101623
1) Solve:
{{{(x+1)/(x+4)+(x-3)/(x+5) = (2x^2+6x+11)/(x^2+9x+20)}}} Add the fractions on the left side.
{{{((x+5)(x+1)+(x-3)(x+4))/(x+4)(x+5) = (2x^2+6x+11)/(x^2+9x+20)}}} Expand the numerator and the denominator on the left side.
{{{((x^2+6x+5)+(x^2+x-12))/(x^2+9x+20) = (2x^2+6x+11)/(x^2+9x+20)}}} Multiply both sides by the denominator.
{{{x^2+6x+5+x^2+x-12 = 2x^2+6x+11}}} Simplify the left side.
{{{2x^2+7x-7 = 2x^2+6x+11}}} Subtract {{{2x^2}}}from both sides.
{{{7x-7 = 6x+11}}} Subtract 6x from both sides.
{{{x-7 = 11}}} Add 7 to both sides.
{{{x = 18}}}