Question

Please help

1.
(05.08 MC)
Given the equation `1/(x-1)+2/x=x/(x-1)`



Part A: What values of x that would make the equation no solution? Why?

Part B: What is the solution of the equation. Show all of your steps.

(10 points)




2.
(05.09 MC)
Max and Maggie have to clean the house. It takes Max 10 hours to clean the house, while Maggie can complete the task in 6 hours. How long will it take for them to work together? Explain each step in solving this equation. (10 points)

Answer 1

Part A)
we have that
1/(x-1)+2/x=x/(x-1)
we know that
for x=1 and x=0 the equation is undefined because the denominator can not be zero

Part B)
1/(x-1)+2/x=x/(x-1) ---------> [x+2*(x-1)]/[x*(x-1)]=x/(x-1)
the term (x-1) in the denominator is simplified
[x+2*(x-1)]/x=x
x+2x-2=x²--------------> x²-3x+2=0

using a graph tool---------> I solve the quadratic equation
see the attache figure
the solution are
x1=1
x2=2

Part C)
we Know that
Max-----------------> takes 10 hours to clean the house
we calculate how much clean in an hour
if takes 10 hour------------> 100%
1 hour----------------------X
X=100/10--------> X=10%

Maggie-------------> takes 6 hours to clean the house
we calculate how much clean in an hour
if takes 6 hour------------> 100%
1 hour----------------------X
X=100/6--------> X=16.67%


we add both percentages
(10+16.67)=26.67 %
if both takes 1 hour----------> 26.67 %
X----------------------------------> 100%
X=100/26.67----------> X=3.75 hours---------> 3 hours+45 minutes

the answer part C) is 3.75 hours (3 hours+45 minutes)