Decompose the rational function \( \frac{7}{x^{2} - 5x + 6} \) into its partial fractions.

4) Dado el dominio de cada función, determina el recorrido. \( \begin{array}{ll}\text { a. } f(x)=20 x \text { y } \operatorname{Dom}(f)=\{0,1,2,3\} & \text { b. } g(x)=-5 x \text { y } \operatorname{Dom}(g)=\{0,3,6,9\} \\ \text { c. } h(x)=x-3 \text { y } \operatorname{Dom}(h)=\{-2,-1,0,1\} & \text { d. } j(x)=3 x+4 \text { y } \operatorname{Dom}(j)=\{0,5,10,15\}\end{array} \)

Solve the following equations and inequalities analytically. Support your solutions graphically. \( \begin{array}{lll}\begin{array}{ll}\text { (a) }|2 x+1|+3=5 & \text { (b) }|2 x+1|+3 \leq 5 \\ \text { (c) }|2 x+1|+3 \geq 5\end{array} \\ \text { A. The solution set is the finite set of real numbers }\{ \\ \text { (a) Find the solution for }|2 x+1|+3=5 \text {. Select the correct choice below, and fill in the } \\ \text { answer box if necessary. } \\ \text { expression. Use a comma to separate answers as needed.) } \\ \text { B. The solution set is the interval } \square \text {. } \\ \text { (Type your answer in interval notation. Use integers or fractions for any } \\ \text { numbers in the expression.) } \\ \text { C. The solution set is } \varnothing \text {. }\end{array} \).

b. Two consecufive number are sucl that the sum of thrice the smaller and twice the larger is 17. Find, correct to three significant figures the smaller number as a percen - tage of the sum of the. two numbers.

A. \( 4 x^{2} y\left(x z^{2}+5 w x y+3\right) \).

(a) Find the solution for \( |2 x+1|+3=5 \). Select the correct choice below, and fill in the answer box if necessary. A. The solution set is the finite set of real numbers \( \{ \). (Simplify your answer. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) B. The solution set is the interval (Type your answer in interval notation. Use integers or fractions for any numbers in the expression.)