Of course! Let's work through the problem step by step.
We are given the expression [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex]:
[tex]\[ y = \left( \frac{x - 1}{x + 2} \right)^3 \][/tex]
To find the simplified form of this expression, we'll break it down into steps:
### Step 1: Identify the Basic Fraction
First, recognize that we have a fraction raised to a power. The basic fraction here is:
[tex]\[ \frac{x - 1}{x + 2} \][/tex]
### Step 2: Apply the Exponent
Next, we need to raise this fraction to the third power. When raising a fraction to a power, we raise both the numerator and the denominator to that power. So, we have:
[tex]\[ \left( \frac{x - 1}{x + 2} \right)^3 = \frac{(x - 1)^3}{(x + 2)^3} \][/tex]
### Step 3: Final Expression
Now that we have raised both the numerator and the denominator to the third power, our final simplified expression is:
[tex]\[ y = \frac{(x - 1)^3}{(x + 2)^3} \][/tex]
Thus, the simplified form of the given expression [tex]\( y = \left( \frac{x - 1}{x + 2} \right)^3 \)[/tex] is:
[tex]\[ y = \frac{(x - 1)^3}{(x + 2)^3} \][/tex]
