# Simplify \frac{1+\frac{2}{x+4}}{1+\frac{9}{x-3}} Step 1: Find the LCM of the denominators of the fractions in the numerator and denominator. Step 2: Multiply the numerator and denominator of the complex fraction by the LCM. Step 3: Factor \frac{x-3}{x+4} Step 4: Divide out common factors.

Simplify.
$\frac{1+\frac{2}{x+4}}{1+\frac{9}{x-3}}$
Step 1: Find the LCM of the denominators of the fractions in the numerator and denominator.
Step 2: Multiply the numerator and denominator of the complex fraction by the LCM.
Step 3: Factor $\frac{x-3}{x+4}$
Step 4: Divide out common factors.
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Given fraction is:
$\frac{1+\frac{2}{x+4}}{1+\frac{9}{x-3}}$
To simplify the given fraction.
Step1. Find the LCM of the denominators of the fractions in numerators and denominators
$\frac{1+\frac{2}{x+4}}{1+\frac{9}{x-3}}=\frac{\frac{\left(x+4\right)+2}{\left(x+4\right)}}{\frac{\left(x-3\right)+9}{\left(x-3\right)}}$
$\frac{\frac{\left(x+6\right)}{\left(x+4\right)}}{\frac{\left(x+6\right)}{x-3}}$
Step 2. Multiply the numerator and denominator of the complex fraction by the LCM.
$\frac{\frac{\left(x+6\right)}{\left(x+4\right)}}{\frac{\left(x+6\right)}{x-3}}=\frac{\left(x+6\right)×\left(x-3\right)}{\left(x+4\right)×\left(x+6\right)}$
Step 3. Factor
$\frac{\left(x+6\right)×\left(x-3\right)}{\left(x+4\right)×\left(x+6\right)}$
Step 4. Divide out common factors
$\frac{\left(x+6\right)×\left(x-3\right)}{\left(x+4\right)×\left(x+6\right)}=\left(\frac{x-3}{x+4}\right)$
Thus, the simplified form is $\left(\frac{x-3}{x+4}\right)$.