Solve each of the following rational equations. 3 x+(4)/(x+3)=2 b 1-(5)/(x)-(6)/(x^2)=0 C

## Step 1: Solve the equation \(3x + \frac{4}{x+3} = 2\)<br />### Multiply both sides by \(x+3\) to eliminate the fraction:<br />\[ 3x(x+3) + 4 = 2(x+3) \]<br />### Simplify and solve for \(x\):<br />\[ 3x^2 + 9x + 4 = 2x + 6 \]<br />\[ 3x^2 + 7x - 2 = 0 \]<br />### Solve the quadratic equation using the quadratic formula \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\):<br />\[ x = \frac{-7 \pm \sqrt{49 + 24}}{6} \]<br />\[ x = \frac{-7 \pm \sqrt{73}}{6} \]<br /><br />## Step 2: Solve the equation \(1 - \frac{5}{x} - \frac{6}{x^2} = 0\)<br />### Multiply both sides by \(x^2\) to eliminate the fractions:<br />\[ x^2 - 5x - 6 = 0 \]<br />### Solve the quadratic equation using the quadratic formula \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\):<br />\[ x = \frac{5 \pm \sqrt{25 + 24}}{2} \]<br />\[ x = \frac{5 \pm \sqrt{49}}{2} \]<br />\[ x = \frac{5 \pm 7}{2} \]<br />\[ x = 6 \quad \text{or} \quad x = -1 \]