To solve the equation 23−5x+3=13x+9\frac{2}{3} - \frac{5}{x+3} = \frac{1}{3x+9}32−x+35=3x+91, we can follow these steps:
We start with the equation: 23−5x+3=13x+9 \frac{2}{3} - \frac{5}{x+3} = \frac{1}{3x+9} 32−x+35=3x+91 Notice that 3x+93x + 93x+9 can be factored as 3(x+3)3(x + 3)3(x+3).
Rewrite the equation with a common denominator: 23−5x+3=13(x+3) \frac{2}{3} - \frac{5}{x+3} = \frac{1}{3(x+3)} 32−x+35=3(x+3)1
Multiply both sides by 3(x+3)3(x + 3)3(x+3) to clear the denominators: 2(x+3)−15=1 2(x + 3) - 15 = 1 2(x+3)−15=1
Simplify the equation: 2x+6−15=1 2x + 6 - 15 = 1 2x+6−15=1 2x−9=1 2x - 9 = 1 2x−9=1 2x=10 2x = 10 2x=10 x=5 x = 5 x=5
x=5\boxed{x = 5}x=5
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