Question

1. working alone, it takes ted 9 minutes to sweep a patio. elisa can sweep the same patio in 8 minutes. is it reasonable for both of them to sweep the patio in under 6 minutes? yes or no must show work!$\frac{x}{9}+\frac{x}{8}=1$yes it takes them 4.2 minutesrewrite each of these rational expressions in simplest form as a single fraction.8. $\frac{4a^{2}}{b^{2}} div \frac{3a^{2}}{b} cdot \frac{9a}{b} =$9. $\frac{5y^{3}}{x^{2}} div \frac{15y^{2}}{x} cdot \frac{2x}{y^{2}} =$solve the following, find the lcd first. also, find the restrictions (aka domain or excluded values) of each.10. $f(x) = \frac{2x-3}{x+4} - \frac{1}{x-5} =$lcd:_________restrictions:_______11. $g(x) = \frac{3}{x^{2}-4} - \frac{2}{x-2} =$lcd:_______restrictions:_______simplify each expression. then, find the restricted domain.12. $\frac{5}{(x-6)} + \frac{5}{(x-5)} =$single fraction:_______restricted domain:_______13. $\frac{6}{n+6} + \frac{5}{n+5} =$single fraction:_______restricted domain:_______find the vertical asymptote, horizontal asymptote, domain and range for the following functions. write the asymptotes as equations!14. $f(x) = \frac{1}{x+3} + 5$va: $-3$ ha: $5$domain:_______ range:_______15. $g(x) = \frac{2}{x-4} - 6$va: $+4$ ha: $-6$domain:_______ range:_________

Explanation:

Answer:

1. YES
2. $\frac{12}{b}$
3. $\frac{2x}{3y}$
4. LCD: $(x+4)(x-5)$

RESTRICTIONS: $x
eq -4, 5$
$f(x)=\frac{2x^2-14x+11}{(x+4)(x-5)}$

1. LCD: $(x+2)(x-2)$

RESTRICTIONS: $x
eq -2, 2$
$g(x)=\frac{-2x-1}{(x+2)(x-2)}$

1. Single fraction: $\frac{10x-55}{(x-6)(x-5)}$

Restricted domain: $x
eq 5, 6$

1. Single fraction: $\frac{11n+60}{(n+6)(n+5)}$

Restricted domain: $n
eq -6, -5$

1. VA: $x=-3$

HA: $y=5$
DOMAIN: All real numbers except $x=-3$
RANGE: All real numbers except $y=5$

1. VA: $x=4$

HA: $y=-6$
DOMAIN: All real numbers except $x=4$
RANGE: All real numbers except $y=-6$