# Chapter 5: Chapter 5

Problem 62

Simplify $\quad\\{[1 /(\mathrm{x}-1)]-[1 /(\mathrm{x}-2)]\\} /\\{[1 /(\mathrm{x}-2)]-[1 /(\mathrm{x}-3)]\\}$

Problem 63

Simplify \(\quad[(1 / a)-1 /(a-b)] /[(1 / a)+1 /(a-b)]\)

Problem 64

Simplify \(\\{[x /(x+y)]+[y /(x-y)]\\} /\\{[y /(x+y)]-[x /(x-y)]\\}\)

Problem 65

(A) If \(\mathrm{x}=(\mathrm{c}-\mathrm{ab}) /(\mathrm{a}-\mathrm{b})\), find the value of the expression \(a(x+b)\) (B) Also, if \(\mathrm{x}=(\mathrm{c}-\mathrm{ab}) /(\mathrm{a}-\mathrm{b})\), find the value of the expression \(b x+c\)

Problem 66

When two resistances are installed in an electric circuit in parallel, the reciprocal of the resistance of the system is equal to the sum of the reciprocals of the parallel resistances. If \(\mathrm{r}_{1}\) and \(\mathrm{r}_{2}\) represent the resistances installed and \(\mathrm{R}\) the resistance of the system, then $1 / \mathrm{R}=1 / \mathrm{r}_{1}+1 / \mathrm{r}_{2}$. What single resistance is the equivalent of resistances of 10 ohms and 25 ohms wired in parallel?