OPERATIONS OF RATIONAL EXPRESSIONS
QUICK QUESTIONS
Question
1
When do you cross multiply?
2
Find the LCM:
3x 5 and
2x
3
Find the LCM:
x − 3 and
x +2
4
Find the LCM: (x +1)2 and (x +1)(x −1)
5
Find the LCM:
6
x 3 + 8 = (x + 2)(
7
Factor: x 2 −1
8
Factor: 3x 2 + 6x
9
Which expression is equivalent to x – 8
4 and
?
x
and
12
13
What factors can cancel?
ANSWER B
When the
denominators are
the same
6x 5
6x 6
(x − 3)(x + 2)
x −6
(x +1)(x −1)
(x +1)2(x −1)
4x3
4x4
2x3
(x
)
4
5
11
10 What is the first step:
+
= −
x
2
x
11
ANSWER A
When a fraction
equals another
fraction.
x −6
x
When solving an equation, why do you
multiply both sides by the LCD?
I should not cancel the (x + 3)’s in the first
fraction. Why not?
x 2 (x + 3)
(x − 1)
+
(x +5)(x + 3) (x + 5)(x + 3)
2
+ 4x + 4
)
(x
2
+ 2x + 4
)
(x +1)(x −1)
(x −1)2
3x(x + 2)
Prime
x+8
– (8 – x)
Make all the
denominators
common
Multiply all
numerators by the
LCD
x
Nothing
To get a common
denominator.
To clear the
denominators.
Because they are
terms and cannot
cancel.
Because you will
ruin all your hard
work.
14
Do you need an LCD?
6x
1
i
(x + 4) x(x + 4)
Yes
No
15
Do you need an LCD?
8(x + 3)
x2
+
x
(x + 3)
Yes
No
16
Do you need an LCD?
Yes
No
17
When can you clear the denominators?
When solving
When adding
x +2
x(x + 2)
WHAT IS THE NEXT STEP?
1.
3.
6 −
8
=
x−5
3
x
2.
A. Cross multiply.
A. Cancel out the x’s.
B. Find the LCD.
B. Get a common denominator.
C. Subtract.
C. Multiply by the LCD.
x2 = 2x + 35
4.
A. Combine x2 and x.
12 + 3
x −1
x 2 −1
A. Multiply by the LCD.
B. Factor, zero product property.
5.
3
1
12
−
=
x
2
x
C. Set the equation equal to 0.
B. Cross multiply.
D. Square root both sides.
C. Factor and make the denominators
common.
3
10x
i 3
x(x + 2) x
6.
x −2 = 3
x +2 x
A. Cross multiply.
A. Cancel out the x’s.
B. Cancel common factors.
B. Multiply by the LCD.
C. Cross multiply.
C. Multiply by the LCD.
D. Get a common denominator.
7.
x2 – 5x – 8 = 3x – 15
8.
x=4
A. Combine like terms.
A. Check for extraneous solutions.
B. Move all terms to one side and leave
“0” on the other side.
B. Don't forget the
C. Divide both sides by x and then
combine like terms.
± sign!
C. Circle your answer, you are done –
yay!