Find all the solutions to

\frac{x+4}{x+5} = \frac{x-3}{2} + \frac{x + 7}{5}

RedDragonl Jul 11, 2024

#1**+2 **

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! :)

NotThatSmart Jul 11, 2024