the statement sec __ nt is wrong. Roll No statement be SCHOOL GRADE 11TH FIRST SEMESTER MATHS TEST-2 C3.The simplified domain Prh(x)=metex is correct and false if f frrm of r (2) 2x-15^2, fxin ard false ir (h) if false ir (h __ unction is never crossis horizontal asymptote. 4. The staph of (x^2-6x+9)/(x^2)-x-6div (2x-6)/(x+2)=(1)/(2),xneq -2& xneq 3 ationer from the given 6. The solution set of the rations!equation of (2)/(x+2)-(1)/(x-2)=(-4)/(x^2)-4 8. C. 2 D. 13 tet (f(x))/(Ehoose) Then f has a hole at x x=1 __ The simplified form of the rational expression of 7. Which of the following is the partial fraction of the decomposition of rational expression A. -2,2 B. -2 A. (3)/(x+2)+(2)/(x-1) C. (-2)/(x+2)+(3)/(x-1) A. x-3 __ f(x)=(x^2-x-6)/(x^2)-4 is a rational function.then which one of the following is not true? D. (3)/(x-2)+(2)/(x+1) (5x-4)/(x^2)-x-2 A. The domain of f is Rvert pm 2 B. (2)/(x-2)+(3)/(x+1) (x^3-27)/(x^2)-9times (x+3)/(x^2)+3x+9,pm 3 C. x=2 is V.A and y=1 is H.A __ clean the whole school rooms, if they working together? rooms in 6hours and Genet can do the same job in 12hours How long will it take asxarrow pm infty ,f(x)arrow 1 B. The graph has an x-intercept at x=2 8 x=-3 III. Show the necessary steps clearly and briefly 11. Write the behaviors of the given rational function of A. 2hrs B. 3hrs f(x)=(x-1)/(x+2) and sketch the graph of the function C. 4hrs D. 6hrs

Let's address each part of the provided content:1. **Simplified Rational Expression**: - The expression given is . - Simplify it step-by-step: - Factorize: - \(x^2 - 6x + 9 = (x-3)^2\) - \(x^2 - x - 6 = (x-3)(x+2)\) - \(2x - 6 = 2(x-3)\) - Rewrite the division as multiplication by the reciprocal: - Cancel common factors: - Therefore, the simplified form is , and the condition & ensures no division by zero.2. **Solution Set of Rational Equation**: - Solve . - Recognize that \(x^2 - 4 = (x+2)(x-2)\). - Combine terms over a common denominator: - Equate numerators since denominators are equal: - Check if is valid in the original equation. Since makes the denominator zero, it is not in the domain. - Thus, the solution set is empty.3. **Partial Fraction Decomposition**: - For the expression , factor the denominator: - \(x^2 - x - 2 = (x-2)(x+1)\). - The partial fraction decomposition is: - Solving for and : - Expand and equate coefficients to solve for and .4. **Work Problem**: - Eden's rate: rooms per hour. - Genet's rate: rooms per hour. - Combined rate: . - Time taken together: hours.5. **Behavior of Rational Function**: - For \(f(x) = \frac{x-1}{x+2}\): - Vertical asymptote at . - Horizontal asymptote as is . - X-intercept at .These solutions cover the mathematical problems presented in your text. If you have any specific questions or need further clarification on any part, feel free to ask!