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Let’s check out your problem:
ii)
1
3
(
2
3
−
1
3
)
\frac{1}{\sqrt{3}}\left(2 \sqrt{3}-\frac{1}{\sqrt{3}}\right)
3
1
(
2
3
−
3
1
)
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Home
Math Problems
Algebra 1
Evaluate integers raised to rational exponents
Full solution
Q.
ii)
1
3
(
2
3
−
1
3
)
\frac{1}{\sqrt{3}}\left(2 \sqrt{3}-\frac{1}{\sqrt{3}}\right)
3
1
(
2
3
−
3
1
)
Distribute fraction:
Distribute the
fraction
(
1
)
/
(
3
)
(1)/(\sqrt{3})
(
1
)
/
(
3
)
across the terms inside the parentheses.
\newline
(
1
)
/
(
3
)
×
2
3
−
(
1
)
/
(
3
)
×
(
1
)
/
(
3
)
(1)/(\sqrt{3}) \times 2\sqrt{3} - (1)/(\sqrt{3}) \times (1)/(\sqrt{3})
(
1
)
/
(
3
)
×
2
3
−
(
1
)
/
(
3
)
×
(
1
)
/
(
3
)
Multiply terms:
Multiply the terms.
\newline
1
3
×
2
3
=
2
\frac{1}{\sqrt{3}} \times 2\sqrt{3} = 2
3
1
×
2
3
=
2
\newline
1
3
×
1
3
=
1
3
\frac{1}{\sqrt{3}} \times \frac{1}{\sqrt{3}} = \frac{1}{3}
3
1
×
3
1
=
3
1
\newline
So, the expression becomes:
\newline
2
−
1
3
2 - \frac{1}{3}
2
−
3
1
Subtract fractions:
Subtract the
fractions
.
\newline
Since
2
2
2
is the same as
6
3
\frac{6}{3}
3
6
, we can write:
\newline
(
6
3
)
−
(
1
3
)
=
(
5
3
)
(\frac{6}{3}) - (\frac{1}{3}) = (\frac{5}{3})
(
3
6
)
−
(
3
1
)
=
(
3
5
)
Check for simplification:
Check the result for any possible simplification.
\newline
The fraction
(
5
3
)
(\frac{5}{3})
(
3
5
)
is already in its simplest form.
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