Sure! Let's solve the given expression step-by-step.
The given expression is:
[tex]\[
\frac{\mu^x + 9 \times \mu^x + \mu^{x+1}}{\mu^{x+\mu} - \mu^x + \mu \times \mu^x}
\][/tex]
### Step 1: Simplify the Numerator
First, let's simplify the numerator [tex]\(\mu^x + 9 \times \mu^x + \mu^{x+1}\)[/tex].
- [tex]\(\mu^x\)[/tex] is a common term in the first two parts, so we can combine them:
[tex]\[
\mu^x + 9 \times \mu^x = (1 + 9) \times \mu^x = 10 \times \mu^x
\][/tex]
- Now, adding the remaining term [tex]\(\mu^{x+1}\)[/tex]:
[tex]\[
10 \times \mu^x + \mu^{x+1}
\][/tex]
Thus, the numerator simplifies to:
[tex]\[
10 \times \mu^x + \mu^{x+1}
\][/tex]
### Step 2: Simplify the Denominator
Now, let's simplify the denominator [tex]\(\mu^{x+\mu} - \mu^x + \mu \times \mu^x\)[/tex].
- We first rewrite [tex]\(\mu \times \mu^x\)[/tex] using the properties of exponents:
[tex]\[
\mu \times \mu^x = \mu^{1+x}
\][/tex]
- So the entire denominator is:
[tex]\[
\mu^{x+\mu} - \mu^x + \mu^{1+x}
\][/tex]
Thus, the denominator is:
[tex]\[
\mu^{x+\mu} - \mu^x + \mu^{1+x}
\][/tex]
### Step 3: Combine the Results
Now that we have simplified both the numerator and the denominator, we can write the final expression:
[tex]\[
\frac{10 \times \mu^x + \mu^{x+1}}{\mu^{x+\mu} - \mu^x + \mu^{1+x}}
\][/tex]
### Step 4: Final Result
So, the simplified form of the given expression is:
[tex]\[
\frac{10 \mu^x + \mu^{x+1}}{\mu^{x+\mu} - \mu^x + \mu^{x+1}}
\][/tex]
This completes our step-by-step simplification of the given expression.
