Question

Find the value of x​

Answer 1

Answer:

$x=-2$

Step-by-step explanation:

First we find their common denominator, which is: $\left(x+5\right)\left(x-4\right)\left(x-2\right)$

We get something like this:$\frac{x+6}{x+5}\left(x+5\right)\left(x-4\right)\left(x-2\right)-\frac{2x-1}{x-4}\left(x+5\right)\left(x-4\right)\left(x-2\right)+\frac{x+4}{x-2}\left(x+5\right)\left(x-4\right)\left(x-2\right)=0$Now we simplify:

$\left(x+6\right)\left(x-4\right)\left(x-2\right)-\left(2x-1\right)\left(x+5\right)\left(x-2\right)+\left(x+4\right)\left(x+5\right)\left(x-4\right)=0$

After that we expand the simplified equation:

$-21x-42=0$

Then we solve!

$-21x-42+42=0+42$

$-21x=42$

$\frac{-21x}{-21}=\frac{42}{-21}$

At last we got the final answer.

$x=-2$

Hope that helps!