1. Simplify the rational expression (4y^2-4)/(6y^2+2y-4) Identify any non-permissible values
2.Create a rational expression with a variable m that has non-permissible values of 3 and –1.
3.Create a rational expression with a variable m that has non-permissible values of 3 and –1.
4.Speed is determined by dividing the distance travelled by the time taken to travel the
distance or s= d/t. Write a rational expression for speed, given the distance travelled,
is 3p^2+5p-2 and the time to travel that distance is 3p^2+2p-1. Identify any nonpermissible values.
5. (5p^2+4)/(p^2-p+4) Indicate any nonpermissible values.
6.Adding, subtracting, multiplying, and dividing rational expressions is similar to performing the same operations on rational numbers. Using examples for each operation, support this statement.
7.Jules is training for a marathon. She finds that for the first 5 km of her training run, she runs at a constant speed of x km/h. For the remaining 7 km of her training run, her speed reduces
by 5 km/h. Write an algebraic expression for the total time Jules takes to run 12 km. Recall that s=t/d.
8.Write a simplified expression, in terms of c, for the area of the given right triangle. Line AB=(c-1)/(c^2-c-12) and line BC= (c+3)/(c^2-5c+4)
9.The sum of the reciprocals of two positive consecutive integers is 240/31 .
a. Explain what each of the expressions represents in this problem.
i) x
ii) x+1
iii) 1/x
iv) 1/(x+1)
V) [(1/x)+(1/(x+1))]
B. Solve the problem. Verify the solution.
10. Jes makes 4 pizzas on her own in 20 minutes, whereas Kyle, on his own, makes 4 pizzas in 30 minutes. How long, in minutes, does it take Jes and Kyle to make 20 pizzas when they work together?
11. (2x-31)/(x^2-49) . Identify any nonpermissible values.
12.Using an example, explain why non-permissible values must be noted before simplifying rational expressions and equations
13. Hannah and Jenna are both travelling to a volleyball tournament in Grande Prairie, and leave at the same time. Hannah’s parents drive her from Edmonton to Grande Prairie, a distance of 460 km. Jenna’s team takes a bus from Dawson Creek, BC to Grande Prairie, a distance of 130 km. Hannah’s parents’ vehicle travels 10 km/h faster than Jenna’s, and Jenna arrives at the tournament 3 hours earlier than Hannah. Determine how fast Hannah’s parents are driving
any help at all would be greatly appreciated (:
#1. (4y^2-4)/(6y^2+2y-4)
= 4(y+1)(y-1) / 2(y+1)(3y-2)
= 2(y-1)/(3y-2)
so y = 2/3 is not allowed, because division by zero is undefined.
#2. 1 / (m+1)(m-3)
Now you try a few and we can check your work.
1. To simplify the rational expression (4y^2-4)/(6y^2+2y-4), we can factor the numerator and denominator:
Numerator: 4y^2-4
Factor out a 4: 4(y^2-1)
Factor as a difference of squares: 4(y-1)(y+1)
Denominator: 6y^2+2y-4
Factor out a 2: 2(3y^2+y-2)
Factor the quadratic: 2(3y-2)(y+1)
Now we can cancel out common factors:
(4(y-1)(y+1))/(2(3y-2)(y+1))
The non-permissible value in this case is -1, because it would cause division by zero in the denominator.