SME
Grade 11 Math · Problem type
Multiply or divide rational expressions
Use this for “Simplify (x − 4)/(x + 1) × (x + 1)/(x − 6)” or a quotient of two such fractions.
Chart
Zero: x = 4
Vertical asymptote x = 6
Horizontal asymptote y = 1
Hole at (−1, 5/7 ≈ 0.7143)
f(2) = 0.5
This is an example. Type your own values to start a new problem.
x
−
x
−
(
)
×
x
−
(
)
x
−
x
Input
example
y
Value of the expression
worked out (not typed)
Formulas
y
=
x
−
a
x
−
b
×
(
x
−
c
x
−
d
)
t
1
2
=
2 − 4
2 − (−1)
×
(
2 − (−1)
2 − 6
)¹
Assumptions
•
To divide, flip the second fraction and multiply: its power becomes −1.
•
Multiply the tops and the bottoms, then cancel a factor that is on both.
•
x can’t make any bottom 0, even one that cancels: those x stay left out.
Step-by-step
WE KNOW
a = 4, b = −1, t = 1, c = −1, d = 6, x = 2
FIND
value of the expression (y)
Step 1 · Find value of the expression (y)
Use y = (x − a) ÷ (x − b) × ((x − c) ÷ (x − d))ᵗ
Multiply tops and bottoms, then cancel the shared factor.
y
=
x
−
a
x
−
d
y
=
2 − 4
2 − 6
(
x
−
4)
x
+ 1
(
x
+ 1)(
x
− 6)
=
x
− 4
x
− 6
,
x
≠
−1,
6
y
=
−
2
−4
y
=
1
2
Check
Put the numbers back in. Both sides should match.
1
2
=
2 − 4
2 − (−1)
×
(
2 − (−1)
2 − 6
)¹
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
Refresh
Related lessons
Rational expressions, equations and functions
Main lesson
Add or subtract rational expressions
Use this for “Write 3/(x − 1) + 2/(x + 4) as one fraction.”
Solve a rational equation
Use this for “Solve x/(x − 2) = 2/(x − 2) + 3/x” and reject the extraneous solution.
Inverse variation
Use this for “6 workers take 10 days. How long do 4 workers take?”