To solve the given expression step-by-step:
Given Expression:
[tex]\[ \frac{(p + q)(r + s)^{4 s s}}{p(r + s) + 9(r + s)} \][/tex]
1. Combine like terms in the denominator:
Notice that the denominator has similar terms \( p(r + s) \) and \( 9(r + s) \). We can factor out \( (r + s) \).
[tex]\[ p(r + s) + 9(r + s) \][/tex]
Factor out \( (r + s) \):
[tex]\[ (r + s)(p + 9) \][/tex]
2. Write the expression with the simplified denominator:
Now the expression becomes:
[tex]\[ \frac{(p + q)(r + s)^{4 s^2}}{(r + s)(p + 9)} \][/tex]
3. Cancel out common terms:
We see that both the numerator and the denominator have a common factor of \( (r + s) \). We can cancel this common factor:
[tex]\[ \frac{(p + q)(r + s)^{4 s^2 - 1}}{p + 9} \][/tex]
4. Simplified Expression:
Now, the expression without the common factors is:
[tex]\[ \frac{(p + q)(r + s)^{4 s^2 - 1}}{p + 9} \][/tex]
Thus, the simplified form of the given expression is:
[tex]\[ \frac{(p + q)(r + s)^{4 s^2 - 1}}{p + 9} \][/tex]
