Solve [16*2n 1 - 4*2n ]/ [16*2n^2 - 2*2n^2 ]

Question

Simplify the expression

\frac{6}{7 n}

Evaluate

\frac{16 \times 2 n \times 1 - 4 \times 2 n}{16 \times 2 n ^{2} - 2 \times 2 n ^{2}}

Multiply the terms

More Steps

Multiply the terms

16 \times 2 n \times 1

Rewrite the expression

16 \times 2 n

Multiply the terms

32 n

\frac{32 n - 4 \times 2 n}{16 \times 2 n ^{2} - 2 \times 2 n ^{2}}

Multiply the terms

\frac{32 n - 8 n}{16 \times 2 n ^{2} - 2 \times 2 n ^{2}}

Multiply the terms

\frac{32 n - 8 n}{32 n ^{2} - 2 \times 2 n ^{2}}

Multiply the terms

\frac{32 n - 8 n}{32 n ^{2} - 4 n ^{2}}

Subtract the terms

More Steps

Simplify

32 n - 8 n

Collect like terms by calculating the sum or difference of their coefficients

(32 - 8) n

Subtract the numbers

24 n

\frac{24 n}{32 n ^{2} - 4 n ^{2}}

Subtract the terms

More Steps

Simplify

32 n^{2} - 4 n^{2}

Collect like terms by calculating the sum or difference of their coefficients

(32 - 4) n^{2}

Subtract the numbers

28 n^{2}

\frac{24 n}{28 n ^{2}}

Use the product rule \frac{a ^{n}}{a ^{m}} = a^{n - m} to simplify the expression

\frac{24}{28 n ^{2 - 1}}

Reduce the fraction

\frac{24}{28 n}

Solution

\frac{6}{7 n}

Show Solution

Find the excluded values

n = 0

Evaluate

\frac{16 \times 2 n \times 1 - 4 \times 2 n}{16 \times 2 n ^{2} - 2 \times 2 n ^{2}}

To find the excluded values,set the denominators equal to 0

16 \times 2 n^{2} - 2 \times 2 n^{2} = 0

Simplify

More Steps

Evaluate

16 \times 2 n^{2} - 2 \times 2 n^{2}

Multiply the terms

32 n^{2} - 2 \times 2 n^{2}

Multiply the terms

32 n^{2} - 4 n^{2}

Collect like terms by calculating the sum or difference of their coefficients

(32 - 4) n^{2}

Subtract the numbers

28 n^{2}

28 n^{2} = 0

Rewrite the expression

n^{2} = 0

Solution

n = 0

Show Solution

Find the roots

n \in \emptyset

Evaluate

\frac{16 \times 2 n \times 1 - 4 \times 2 n}{16 \times 2 n ^{2} - 2 \times 2 n ^{2}}

To find the roots of the expression,set the expression equal to 0

\frac{16 \times 2 n \times 1 - 4 \times 2 n}{16 \times 2 n ^{2} - 2 \times 2 n ^{2}} = 0

Find the domain

More Steps

Evaluate

16 \times 2 n^{2} - 2 \times 2 n^{2} \neq = 0

Simplify

More Steps

Evaluate

16 \times 2 n^{2} - 2 \times 2 n^{2}

Multiply the terms

32 n^{2} - 2 \times 2 n^{2}

Multiply the terms

32 n^{2} - 4 n^{2}

Collect like terms by calculating the sum or difference of their coefficients

(32 - 4) n^{2}

Subtract the numbers

28 n^{2}

28 n^{2} \neq = 0

Rewrite the expression

n^{2} \neq = 0

The only way a power can not be 0 is when the base not equals 0

n \neq = 0

\frac{16 \times 2 n \times 1 - 4 \times 2 n}{16 \times 2 n ^{2} - 2 \times 2 n ^{2}} = 0, n \neq = 0

Calculate

\frac{16 \times 2 n \times 1 - 4 \times 2 n}{16 \times 2 n ^{2} - 2 \times 2 n ^{2}} = 0

Multiply the terms

More Steps

Multiply the terms

16 \times 2 n \times 1

Rewrite the expression

16 \times 2 n

Multiply the terms

32 n

\frac{32 n - 4 \times 2 n}{16 \times 2 n ^{2} - 2 \times 2 n ^{2}} = 0

Multiply the terms

\frac{32 n - 8 n}{16 \times 2 n ^{2} - 2 \times 2 n ^{2}} = 0

Multiply the terms

\frac{32 n - 8 n}{32 n ^{2} - 2 \times 2 n ^{2}} = 0

Multiply the terms

\frac{32 n - 8 n}{32 n ^{2} - 4 n ^{2}} = 0

Subtract the terms

More Steps

Simplify

32 n - 8 n

Collect like terms by calculating the sum or difference of their coefficients

(32 - 8) n

Subtract the numbers

24 n

\frac{24 n}{32 n ^{2} - 4 n ^{2}} = 0

Subtract the terms

More Steps

Simplify

32 n^{2} - 4 n^{2}

Collect like terms by calculating the sum or difference of their coefficients

(32 - 4) n^{2}

Subtract the numbers

28 n^{2}

\frac{24 n}{28 n ^{2}} = 0

Divide the terms

More Steps

Evaluate

\frac{24 n}{28 n ^{2}}

Use the product rule \frac{a ^{n}}{a ^{m}} = a^{n - m} to simplify the expression

\frac{24}{28 n ^{2 - 1}}

Reduce the fraction

\frac{24}{28 n}

Cancel out the common factor 4

\frac{6}{7 n}

\frac{6}{7 n} = 0

Cross multiply

6 = 7 n \times 0

Simplify the equation

6 = 0

Solution

n \in \emptyset

Show Solution