Solve each of the following equations. Be sure to check your solutions.

1. $3+\frac{2x}{x+1}=5x$ 

   Hint (a):

   To remove the denominator, multiply both sides of (or each term in) the equation by $\left(x + 1\right)$.

2. $x^{2} + 6x + 9 = 2x^{2} + 3x + 5$ 

   Answer (b):

   $x = 4, −1$

3. $8-\sqrt{9-2x}=x+3$ 

   Step 1 (c):

   Subtract $8$ from both sides and divide both sides by $−1$.

   $\sqrt{9-2x}=5-x$

   Answer (c):

   After setting the resulting equation equal to zero and solving the quadratic equation, $x = 4$.

   Step 2 (c):

   Square both sides and simplify.

   $\left(\sqrt{9-2x}\right)^{2}=(5-x)^2$

   $9 − 2x = x^{2} − 10x + 25$