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avatar+826 

Find all the solutions to
\frac{x+4}{x+5} = \frac{x-3}{2} + \frac{x + 7}{5}

 Jul 11, 2024
 #1
avatar+1926 
+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! :)

 Jul 11, 2024

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