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Simplify (5(a+ square root of 2))/(2a- square root of 3)
5
(
a
+
√
2
)
2
a
-
√
3
Step 1
Multiply
5
(
a
+
√
2
)
2
a
-
√
3
by
2
a
+
√
3
2
a
+
√
3
.
5
(
a
+
√
2
)
2
a
-
√
3
⋅
2
a
+
√
3
2
a
+
√
3
Step 2
Combine
fractions
.
Multiply
5
(
a
+
√
2
)
2
a
-
√
3
by
2
a
+
√
3
2
a
+
√
3
.
5
(
a
+
√
2
)
(
2
a
+
√
3
)
(
2
a
-
√
3
)
(
2
a
+
√
3
)
Expand the
denominator
using the
FOIL
method.
5
(
a
+
√
2
)
(
2
a
+
√
3
)
4
a
2
+
2
a
√
3
-
2
√
3
a
-
√
3
2
Simplify.
Rewrite
√
3
2
as
3
.
Use
n
√
a
x
=
a
x
n
to rewrite
√
3
as
3
1
2
.
5
(
a
+
√
2
)
(
2
a
+
√
3
)
4
a
2
-
(
3
1
2
)
2
Apply the
power rule
and
multiply
exponents
,
(
a
m
)
n
=
a
m
n
.
5
(
a
+
√
2
)
(
2
a
+
√
3
)
4
a
2
-
3
1
2
⋅
2
Combine
1
2
and
2
.
5
(
a
+
√
2
)
(
2
a
+
√
3
)
4
a
2
-
3
2
2
Cancel the
common factor
of
2
.
Cancel the
common factor
.
5
(
a
+
√
2
)
(
2
a
+
√
3
)
4
a
2
-
3
2
2
Rewrite the
expression
.
5
(
a
+
√
2
)
(
2
a
+
√
3
)
4
a
2
-
3
1
5
(
a
+
√
2
)
(
2
a
+
√
3
)
4
a
2
-
3
1
Evaluate
the
exponent
.
5
(
a
+
√
2
)
(
2
a
+
√
3
)
4
a
2
-
1
⋅
3
5
(
a
+
√
2
)
(
2
a
+
√
3
)
4
a
2
-
1
⋅
3
Multiply
-
1
by
3
.
5
(
a
+
√
2
)
(
2
a
+
√
3
)
4
a
2
-
3
5
(
a
+
√
2
)
(
2
a
+
√
3
)
4
a
2
-
3
Group
2
a
+
√
3
and
a
+
√
2
together.
5
(
(
2
a
+
√
3
)
(
a
+
√
2
)
)
4
a
2
-
3
5
(
(
2
a
+
√
3
)
(
a
+
√
2
)
)
4
a
2
-
3
Step 3
Expand
(
2
a
+
√
3
)
(
a
+
√
2
)
using the
FOIL
Method.
Apply the
distributive property
.
5
(
2
a
(
a
+
√
2
)
+
√
3
(
a
+
√
2
)
)
4
a
2
-
3
Apply the
distributive property
.
5
(
2
a
⋅
a
+
2
a
√
2
+
√
3
(
a
+
√
2
)
)
4
a
2
-
3
Apply the
distributive property
.
5
(
2
a
⋅
a
+
2
a
√
2
+
√
3
a
+
√
3
√
2
)
4
a
2
-
3
5
(
2
a
⋅
a
+
2
a
√
2
+
√
3
a
+
√
3
√
2
)
4
a
2
-
3
Step 4
Simplify
terms
.
Simplify each
term
.
Multiply
a
by
a
by adding the
exponents
.
Move
a
.
5
(
2
(
a
⋅
a
)
+
2
a
√
2
+
√
3
a
+
√
3
√
2
)
4
a
2
-
3
Multiply
a
by
a
.
5
(
2
a
2
+
2
a
√
2
+
√
3
a
+
√
3
√
2
)
4
a
2
-
3
5
(
2
a
2
+
2
a
√
2
+
√
3
a
+
√
3
√
2
)
4
a
2
-
3
Combine
using the
product rule
for radicals.
5
(
2
a
2
+
2
a
√
2
+
√
3
a
+
√
3
⋅
2
)
4
a
2
-
3
Multiply
3
by
2
.
5
(
2
a
2
+
2
a
√
2
+
√
3
a
+
√
6
)
4
a
2
-
3
5
(
2
a
2
+
2
a
√
2
+
√
3
a
+
√
6
)
4
a
2
-
3
Reorder
terms
.
5
(
2
a
2
+
2
a
√
2
+
a
√
3
+
√
6
)
4
a
2
-
3
5
(
2
a
2
+
2
a
√
2
+
a
√
3
+
√
6
)
4
a
2
-
3
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