Rational Expressions & Equations — Drills
Rational Expressions & Equations has 6 drill skills. Each one generates fresh questions every time, with a hint and full worked steps, so you can keep practising a single skill until it settles.
What these drills cover
These questions use 10 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.
- Ratio — A comparison of two quantities, like 3 cups flour to 2 cups water.
- Rate — A ratio of two different units, like miles per hour or dollars per pound.
- Reciprocal — The flip of a fraction. The reciprocal of 35 is 53.
- LCD — Least common denominator — the smallest number both denominators divide into.
- Factor — A number that divides evenly into another.
- Asymptote — A line the graph approaches but never reaches — here, the x-axis.
- Leading coefficient — The number in front of the highest power. Its sign decides which way the right end goes.
- Domain restriction — A square root needs its inside to be ≥ 0, which limits the inputs allowed.
- Vertical asymptote — A vertical line the graph approaches but never reaches, at an excluded value that does not cancel.
- Horizontal asymptote — The height the graph settles towards far out to the left and right.
Exclude
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
What value must be excluded from 5x - 6?
Worked answer
6
x - 6 = 0
x=6
Problem 2
What value must be excluded from 5x + 4?
Worked answer
-4
x + 4 = 0
x=-4
Simplifying
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Simplify x2-36x+6.
Worked answer
x-6
(x-6)(x+6)x+6
Cancel the shared factor
Problem 2
Simplify x2-64x+8.
Worked answer
x-8
(x-8)(x+8)x+8
Cancel the shared factor
Adding
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Simplify 2x+7x.
Worked answer
9/x
2+7x
=9x
Problem 2
Simplify 5x+6x.
Worked answer
11/x
5+6x
=11x
Solving
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Solve x6+x4=5.
Worked answer
12
2x+3x=60
5x=60
x=12
Problem 2
Solve x2+x4=6.
Worked answer
8
2x+1x=24
3x=24
x=8
Work
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
One pipe fills a tank in 4 hours, another in 12. How many hours together?
Worked answer
3
14+112=1648
That is 1648 of a tank per hour
So 3 hours
Problem 2
One pipe fills a tank in 6 hours, another in 12. How many hours together?
Worked answer
4
16+112=1872
That is 1872 of a tank per hour
So 4 hours
Asymptote
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Give the vertical asymptote of y=x+6x + 3 as a value of x.
Worked answer
-3
x + 3 = 0 at x=-3
The top is not zero there, so it is an asymptote
Problem 2
Give the vertical asymptote of y=x+2x - 5 as a value of x.
Worked answer
5
x - 5 = 0 at x=5
The top is not zero there, so it is an asymptote