The original expression seems to contain errors. Here is the corrected version:

[tex]\[
\frac{(p+q)(r+s)^{4}}{p(r+s)+9(r+s)}
\][/tex]

Make sure to use proper LaTeX formatting to ensure the expression is clear and correct.



Answer :

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]