Questions: Solve for (x). [ frac23-frac5x+3=frac13 x+9 x= ]

Solve for (x).
[
frac23-frac5x+3=frac13 x+9 
x=
]
Transcript text: Solve for $x$. \[ \begin{array}{l} \frac{2}{3}-\frac{5}{x+3}=\frac{1}{3 x+9} \\ x= \end{array} \] Question Help: Video eBook Written Example Submit Question
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Solution

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Solution Steps

To solve the equation 235x+3=13x+9\frac{2}{3} - \frac{5}{x+3} = \frac{1}{3x+9}, we can follow these steps:

  1. Recognize that 3x+93x + 9 can be factored as 3(x+3)3(x + 3).
  2. Rewrite the equation with a common denominator.
  3. Solve the resulting equation for xx.
Step 1: Recognize the Common Denominator

We start with the equation: 235x+3=13x+9 \frac{2}{3} - \frac{5}{x+3} = \frac{1}{3x+9} Notice that 3x+93x + 9 can be factored as 3(x+3)3(x + 3).

Step 2: Rewrite the Equation

Rewrite the equation with a common denominator: 235x+3=13(x+3) \frac{2}{3} - \frac{5}{x+3} = \frac{1}{3(x+3)}

Step 3: Clear the Denominators

Multiply both sides by 3(x+3)3(x + 3) to clear the denominators: 2(x+3)15=1 2(x + 3) - 15 = 1

Step 4: Simplify and Solve for xx

Simplify the equation: 2x+615=1 2x + 6 - 15 = 1 2x9=1 2x - 9 = 1 2x=10 2x = 10 x=5 x = 5

Final Answer

x=5\boxed{x = 5}

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