Solve \frac{11r^4r}{8r-3r}

Question

Simplify the expression

\frac{11 r ^{4}}{5}

Evaluate

\frac{11 r ^{4} \times r}{8 r - 3 r}

Multiply

More Steps

Multiply the terms

11 r^{4} \times r

Multiply the terms with the same base by adding their exponents

11 r^{4 + 1}

Add the numbers

11 r^{5}

\frac{11 r ^{5}}{8 r - 3 r}

Subtract the terms

More Steps

Simplify

8 r - 3 r

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

(8 - 3) r

Subtract the numbers

5 r

\frac{11 r ^{5}}{5 r}

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

\frac{11 r ^{5 - 1}}{5}

Solution

\frac{11 r ^{4}}{5}

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Find the excluded values

r = 0

Evaluate

\frac{11 r ^{4} \times r}{8 r - 3 r}

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

8 r - 3 r = 0

Subtract the terms

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Evaluate

8 r - 3 r

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

(8 - 3) r

Subtract the numbers

5 r

5 r = 0

Solution

r = 0

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Find the roots

r \in \emptyset

Evaluate

\frac{11 r ^{4} \times r}{8 r - 3 r}

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

\frac{11 r ^{4} \times r}{8 r - 3 r} = 0

Find the domain

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Evaluate

8 r - 3 r \neq = 0

Subtract the terms

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Evaluate

8 r - 3 r

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

(8 - 3) r

Subtract the numbers

5 r

5 r \neq = 0

Rewrite the expression

r \neq = 0

\frac{11 r ^{4} \times r}{8 r - 3 r} = 0, r \neq = 0

Calculate

\frac{11 r ^{4} \times r}{8 r - 3 r} = 0

Multiply

More Steps

Multiply the terms

11 r^{4} \times r

Multiply the terms with the same base by adding their exponents

11 r^{4 + 1}

Add the numbers

11 r^{5}

\frac{11 r ^{5}}{8 r - 3 r} = 0

Subtract the terms

More Steps

Simplify

8 r - 3 r

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

(8 - 3) r

Subtract the numbers

5 r

\frac{11 r ^{5}}{5 r} = 0

Divide the terms

More Steps

Evaluate

\frac{11 r ^{5}}{5 r}

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

\frac{11 r ^{5 - 1}}{5}

Reduce the fraction

\frac{11 r ^{4}}{5}

\frac{11 r ^{4}}{5} = 0

Simplify

11 r^{4} = 0

Rewrite the expression

r^{4} = 0

The only way a power can be 0 is when the base equals 0

r = 0

Check if the solution is in the defined range

r = 0, r \neq = 0

Solution

r \in \emptyset

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