+826 Find all the solutions to
\frac{x+4}{x+5} = \frac{x-3}{2} + \frac{x + 7}{5}
+1892 First, we want to get rid of the nasty fractions.
Let's do this by multiplying both sides by the LCM of the denominators.
By doing this, we have
\(10\left(x+4\right)=5\left(x-3\right)\left(x+5\right)+2\left(x+7\right)\left(x+5\right)\)
Distributing every number in and moving all terms to one side, we have
\(7x^{2}+24x-45=0\)
Using the quadratic equation and finding what x is, we have
\(x=\frac{3\sqrt{51}-12}{7}\\ x=\frac{-3\sqrt{51}-12}{7}\)
Thanks! :)
