Download x 1 1+ HW: Worksheet

Aim: How do we simplify complex fractions?
1
Do Now: 1. Add: 1 +
x
1
2. Subtract: 1−
x
1
1+
x
3. Simplify:
1
1−
x
HW: Worksheet
There are 2 methods to simplify complex
fractions
We first need to simplified the numerator and
denominator for both methods then do either one
Method 1:
a
a
d
a
c
b = ÷
= ⋅
c b d b c
a
d
ad
b =
Method 2: c
bc
d
ad
=
bc
x+ 1
1
1+
x+ 1 x− 1
x = x
=
÷
1
x
−
1
x
x
1−
x
x
x+ 1
x+ 1 x
=
⋅
=
x x− 1 x− 1
1 x+ 1
1+
x
(
x
+
1
)
x+ 1
x = x =
=
1 x− 1
x
(
x
−
1
)
x− 1
1−
x
x
1 to simplify complex fraction.
2– 5
x
3 + 1x
2x –
= x
3x +
x
5
x
1
x
2x – 5
xSimplify the numerator and
=
3xdenominator.
+1
(Step 1)
x
2x – 5
3x + 1
÷
=
Write as a division problem.
x
x
Multiply by the reciprocal of
x
= 2x – 5 ·
(Step
x
3x. + 1
3x
+ 1 2)
x
=
2x – 5
3x + 1
Multiply and simplify.
(Step 3)
Example: simplify the expression
x + 5x + 6
2
2
x + 5x + 6 x − 9
3 xy
÷
=
=
2
3
xy
6
xy
x −9
2
6 xy
x + 5 x + 6 6 xy
2
3 xy
( x + 2 ) ( x + 3) g 6 xy
3 xy
( x + 3) ( x − 3)
2
⋅
x −9
2
2x + 4
=
x− 3
=
simplify complex fraction.
Method 1
3
x–1
4
x2 – 1
3
x–1
=
4
(x – 1)(x + 1)
=
3
x–1
4
÷ (x – 1)(x + 1)
=
3
x–1
·
= 3(x4+ 1)
(x – 1)(x + 1)
4
3
x–1
4
x2 – 1
Method 2
3
3
x–1
x–1 =
4
4
(x – 1)(x + 1)
x2 – 1
3( x + 1)
=
4
Practice
Simplify.
1)
x x
+
2 3
1
2
1
1+
x
2)
1
1− 2
x
3
(x + 2)(2x − 1)
3)
x
x+ 2