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Simplify (5x-3)/(7x+3)+(8x^2+3)/(7x+1)
5
x
-
3
7
x
+
3
+
8
x
2
+
3
7
x
+
1
Step 1
To write
5
x
-
3
7
x
+
3
as a
fraction
with a
common denominator
,
multiply
by
7
x
+
1
7
x
+
1
.
5
x
-
3
7
x
+
3
⋅
7
x
+
1
7
x
+
1
+
8
x
2
+
3
7
x
+
1
Step 2
To write
8
x
2
+
3
7
x
+
1
as a
fraction
with a
common denominator
,
multiply
by
7
x
+
3
7
x
+
3
.
5
x
-
3
7
x
+
3
⋅
7
x
+
1
7
x
+
1
+
8
x
2
+
3
7
x
+
1
⋅
7
x
+
3
7
x
+
3
Step 3
Write each
expression
with a
common denominator
of
(
7
x
+
3
)
(
7
x
+
1
)
, by multiplying each by an appropriate
factor
of
1
.
Multiply
5
x
-
3
7
x
+
3
by
7
x
+
1
7
x
+
1
.
(
5
x
-
3
)
(
7
x
+
1
)
(
7
x
+
3
)
(
7
x
+
1
)
+
8
x
2
+
3
7
x
+
1
⋅
7
x
+
3
7
x
+
3
Multiply
8
x
2
+
3
7
x
+
1
by
7
x
+
3
7
x
+
3
.
(
5
x
-
3
)
(
7
x
+
1
)
(
7
x
+
3
)
(
7
x
+
1
)
+
(
8
x
2
+
3
)
(
7
x
+
3
)
(
7
x
+
1
)
(
7
x
+
3
)
Reorder the
factors
of
(
7
x
+
3
)
(
7
x
+
1
)
.
(
5
x
-
3
)
(
7
x
+
1
)
(
7
x
+
1
)
(
7
x
+
3
)
+
(
8
x
2
+
3
)
(
7
x
+
3
)
(
7
x
+
1
)
(
7
x
+
3
)
(
5
x
-
3
)
(
7
x
+
1
)
(
7
x
+
1
)
(
7
x
+
3
)
+
(
8
x
2
+
3
)
(
7
x
+
3
)
(
7
x
+
1
)
(
7
x
+
3
)
Step 4
Combine
the
numerators
over the
common denominator
.
(
5
x
-
3
)
(
7
x
+
1
)
+
(
8
x
2
+
3
)
(
7
x
+
3
)
(
7
x
+
1
)
(
7
x
+
3
)
Step 5
Simplify the
numerator
.
Expand
(
5
x
-
3
)
(
7
x
+
1
)
using the
FOIL
Method.
Apply the
distributive property
.
5
x
(
7
x
+
1
)
-
3
(
7
x
+
1
)
+
(
8
x
2
+
3
)
(
7
x
+
3
)
(
7
x
+
1
)
(
7
x
+
3
)
Apply the
distributive property
.
5
x
(
7
x
)
+
5
x
⋅
1
-
3
(
7
x
+
1
)
+
(
8
x
2
+
3
)
(
7
x
+
3
)
(
7
x
+
1
)
(
7
x
+
3
)
Apply the
distributive property
.
5
x
(
7
x
)
+
5
x
⋅
1
-
3
(
7
x
)
-
3
⋅
1
+
(
8
x
2
+
3
)
(
7
x
+
3
)
(
7
x
+
1
)
(
7
x
+
3
)
5
x
(
7
x
)
+
5
x
⋅
1
-
3
(
7
x
)
-
3
⋅
1
+
(
8
x
2
+
3
)
(
7
x
+
3
)
(
7
x
+
1
)
(
7
x
+
3
)
Simplify and
combine
like terms
.
Simplify each
term
.
Rewrite using the
commutative property of multiplication
.
5
⋅
7
x
⋅
x
+
5
x
⋅
1
-
3
(
7
x
)
-
3
⋅
1
+
(
8
x
2
+
3
)
(
7
x
+
3
)
(
7
x
+
1
)
(
7
x
+
3
)
Multiply
x
by
x
by adding the
exponents
.
Move
x
.
5
⋅
7
(
x
⋅
x
)
+
5
x
⋅
1
-
3
(
7
x
)
-
3
⋅
1
+
(
8
x
2
+
3
)
(
7
x
+
3
)
(
7
x
+
1
)
(
7
x
+
3
)
Multiply
x
by
x
.
5
⋅
7
x
2
+
5
x
⋅
1
-
3
(
7
x
)
-
3
⋅
1
+
(
8
x
2
+
3
)
(
7
x
+
3
)
(
7
x
+
1
)
(
7
x
+
3
)
5
⋅
7
x
2
+
5
x
⋅
1
-
3
(
7
x
)
-
3
⋅
1
+
(
8
x
2
+
3
)
(
7
x
+
3
)
(
7
x
+
1
)
(
7
x
+
3
)
Multiply
5
by
7
.
35
x
2
+
5
x
⋅
1
-
3
(
7
x
)
-
3
⋅
1
+
(
8
x
2
+
3
)
(
7
x
+
3
)
(
7
x
+
1
)
(
7
x
+
3
)
Multiply
5
by
1
.
35
x
2
+
5
x
-
3
(
7
x
)
-
3
⋅
1
+
(
8
x
2
+
3
)
(
7
x
+
3
)
(
7
x
+
1
)
(
7
x
+
3
)
Multiply
7
by
-
3
.
35
x
2
+
5
x
-
21
x
-
3
⋅
1
+
(
8
x
2
+
3
)
(
7
x
+
3
)
(
7
x
+
1
)
(
7
x
+
3
)
Multiply
-
3
by
1
.
35
x
2
+
5
x
-
21
x
-
3
+
(
8
x
2
+
3
)
(
7
x
+
3
)
(
7
x
+
1
)
(
7
x
+
3
)
35
x
2
+
5
x
-
21
x
-
3
+
(
8
x
2
+
3
)
(
7
x
+
3
)
(
7
x
+
1
)
(
7
x
+
3
)
Subtract
21
x
from
5
x
.
35
x
2
-
16
x
-
3
+
(
8
x
2
+
3
)
(
7
x
+
3
)
(
7
x
+
1
)
(
7
x
+
3
)
35
x
2
-
16
x
-
3
+
(
8
x
2
+
3
)
(
7
x
+
3
)
(
7
x
+
1
)
(
7
x
+
3
)
Expand
(
8
x
2
+
3
)
(
7
x
+
3
)
using the
FOIL
Method.
Apply the
distributive property
.
35
x
2
-
16
x
-
3
+
8
x
2
(
7
x
+
3
)
+
3
(
7
x
+
3
)
(
7
x
+
1
)
(
7
x
+
3
)
Apply the
distributive property
.
35
x
2
-
16
x
-
3
+
8
x
2
(
7
x
)
+
8
x
2
⋅
3
+
3
(
7
x
+
3
)
(
7
x
+
1
)
(
7
x
+
3
)
Apply the
distributive property
.
35
x
2
-
16
x
-
3
+
8
x
2
(
7
x
)
+
8
x
2
⋅
3
+
3
(
7
x
)
+
3
⋅
3
(
7
x
+
1
)
(
7
x
+
3
)
35
x
2
-
16
x
-
3
+
8
x
2
(
7
x
)
+
8
x
2
⋅
3
+
3
(
7
x
)
+
3
⋅
3
(
7
x
+
1
)
(
7
x
+
3
)
Simplify each
term
.
Rewrite using the
commutative property of multiplication
.
35
x
2
-
16
x
-
3
+
8
⋅
7
x
2
x
+
8
x
2
⋅
3
+
3
(
7
x
)
+
3
⋅
3
(
7
x
+
1
)
(
7
x
+
3
)
Multiply
x
2
by
x
by adding the
exponents
.
Move
x
.
35
x
2
-
16
x
-
3
+
8
⋅
7
(
x
⋅
x
2
)
+
8
x
2
⋅
3
+
3
(
7
x
)
+
3
⋅
3
(
7
x
+
1
)
(
7
x
+
3
)
Multiply
x
by
x
2
.
Raise
x
to the
power
of
1
.
35
x
2
-
16
x
-
3
+
8
⋅
7
(
x
1
x
2
)
+
8
x
2
⋅
3
+
3
(
7
x
)
+
3
⋅
3
(
7
x
+
1
)
(
7
x
+
3
)
Use the
power rule
a
m
a
n
=
a
m
+
n
to
combine
exponents
.
35
x
2
-
16
x
-
3
+
8
⋅
7
x
1
+
2
+
8
x
2
⋅
3
+
3
(
7
x
)
+
3
⋅
3
(
7
x
+
1
)
(
7
x
+
3
)
35
x
2
-
16
x
-
3
+
8
⋅
7
x
1
+
2
+
8
x
2
⋅
3
+
3
(
7
x
)
+
3
⋅
3
(
7
x
+
1
)
(
7
x
+
3
)
Add
1
and
2
.
35
x
2
-
16
x
-
3
+
8
⋅
7
x
3
+
8
x
2
⋅
3
+
3
(
7
x
)
+
3
⋅
3
(
7
x
+
1
)
(
7
x
+
3
)
35
x
2
-
16
x
-
3
+
8
⋅
7
x
3
+
8
x
2
⋅
3
+
3
(
7
x
)
+
3
⋅
3
(
7
x
+
1
)
(
7
x
+
3
)
Multiply
8
by
7
.
35
x
2
-
16
x
-
3
+
56
x
3
+
8
x
2
⋅
3
+
3
(
7
x
)
+
3
⋅
3
(
7
x
+
1
)
(
7
x
+
3
)
Multiply
3
by
8
.
35
x
2
-
16
x
-
3
+
56
x
3
+
24
x
2
+
3
(
7
x
)
+
3
⋅
3
(
7
x
+
1
)
(
7
x
+
3
)
Multiply
7
by
3
.
35
x
2
-
16
x
-
3
+
56
x
3
+
24
x
2
+
21
x
+
3
⋅
3
(
7
x
+
1
)
(
7
x
+
3
)
Multiply
3
by
3
.
35
x
2
-
16
x
-
3
+
56
x
3
+
24
x
2
+
21
x
+
9
(
7
x
+
1
)
(
7
x
+
3
)
35
x
2
-
16
x
-
3
+
56
x
3
+
24
x
2
+
21
x
+
9
(
7
x
+
1
)
(
7
x
+
3
)
Add
35
x
2
and
24
x
2
.
59
x
2
-
16
x
-
3
+
56
x
3
+
21
x
+
9
(
7
x
+
1
)
(
7
x
+
3
)
Add
-
16
x
and
21
x
.
59
x
2
+
5
x
-
3
+
56
x
3
+
9
(
7
x
+
1
)
(
7
x
+
3
)
Add
-
3
and
9
.
59
x
2
+
5
x
+
56
x
3
+
6
(
7
x
+
1
)
(
7
x
+
3
)
Reorder
terms
.
56
x
3
+
59
x
2
+
5
x
+
6
(
7
x
+
1
)
(
7
x
+
3
)
56
x
3
+
59
x
2
+
5
x
+
6
(
7
x
+
1
)
(
7
x
+
3
)
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