Solve (5t^2-(t^2))/(3t-t)

Question

Simplify the expression

2 t

Evaluate

\frac{5 t ^{2} - t ^{2}}{3 t - t}

Subtract the terms

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Simplify

5 t^{2} - t^{2}

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

(5 - 1) t^{2}

Subtract the numbers

4 t^{2}

\frac{4 t ^{2}}{3 t - t}

Subtract the terms

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Simplify

3 t - t

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

(3 - 1) t

Subtract the numbers

2 t

\frac{4 t ^{2}}{2 t}

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

\frac{4 t ^{2 - 1}}{2}

Reduce the fraction

\frac{4 t}{2}

Solution

More Steps

Evaluate

\frac{4}{2}

Reduce the numbers

\frac{2}{1}

Calculate

2

2 t

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Find the excluded values

t = 0

Evaluate

\frac{5 t ^{2} - ( t ^{2} )}{3 t - t}

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

3 t - t = 0

Subtract the terms

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Evaluate

3 t - t

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

(3 - 1) t

Subtract the numbers

2 t

2 t = 0

Solution

t = 0

Show Solution

Find the roots

t \in \emptyset

Evaluate

\frac{5 t ^{2} - ( t ^{2} )}{3 t - t}

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

\frac{5 t ^{2} - ( t ^{2} )}{3 t - t} = 0

Find the domain

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Evaluate

3 t - t \neq = 0

Subtract the terms

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Evaluate

3 t - t

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

(3 - 1) t

Subtract the numbers

2 t

2 t \neq = 0

Rewrite the expression

t \neq = 0

\frac{5 t ^{2} - ( t ^{2} )}{3 t - t} = 0, t \neq = 0

Calculate

\frac{5 t ^{2} - ( t ^{2} )}{3 t - t} = 0

Calculate

\frac{5 t ^{2} - t ^{2}}{3 t - t} = 0

Subtract the terms

More Steps

Simplify

5 t^{2} - t^{2}

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

(5 - 1) t^{2}

Subtract the numbers

4 t^{2}

\frac{4 t ^{2}}{3 t - t} = 0

Subtract the terms

More Steps

Simplify

3 t - t

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

(3 - 1) t

Subtract the numbers

2 t

\frac{4 t ^{2}}{2 t} = 0

Divide the terms

More Steps

Evaluate

\frac{4 t ^{2}}{2 t}

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

\frac{4 t ^{2 - 1}}{2}

Reduce the fraction

\frac{4 t}{2}

Divide the terms

More Steps

Evaluate

\frac{4}{2}

Reduce the numbers

\frac{2}{1}

Calculate

2

2 t

2 t = 0

Rewrite the expression

t = 0

Check if the solution is in the defined range

t = 0, t \neq = 0

Solution

t \in \emptyset

Show Solution