Solve (-10m^385m^2-180m)/(2m-9)

Question

Simplify the expression

- \frac{850 m ^{5} + 180 m}{2 m - 9}

Evaluate

\frac{- 10 m ^{3} \times 85 m ^{2} - 180 m}{2 m - 9}

Multiply

More Steps

Multiply the terms

- 10 m^{3} \times 85 m^{2}

Multiply the terms

- 850 m^{3} \times m^{2}

Multiply the terms with the same base by adding their exponents

- 850 m^{3 + 2}

Add the numbers

- 850 m^{5}

\frac{- 850 m ^{5} - 180 m}{2 m - 9}

Solution

- \frac{850 m ^{5} + 180 m}{2 m - 9}

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Find the excluded values

m = \frac{9}{2}

Evaluate

\frac{- 10 m ^{3} \times 85 m ^{2} - 180 m}{2 m - 9}

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

2 m - 9 = 0

Move the constant to the right-hand side and change its sign

2 m = 0 + 9

Removing 0 doesn't change the value,so remove it from the expression

2 m = 9

Divide both sides

\frac{2 m}{2} = \frac{9}{2}

Solution

m = \frac{9}{2}

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Find the roots

m = 0

Evaluate

\frac{- 10 m ^{3} \times 85 m ^{2} - 180 m}{2 m - 9}

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

\frac{- 10 m ^{3} \times 85 m ^{2} - 180 m}{2 m - 9} = 0

Find the domain

More Steps

Evaluate

2 m - 9 \neq = 0

Move the constant to the right side

2 m \neq = 0 + 9

Removing 0 doesn't change the value,so remove it from the expression

2 m \neq = 9

Divide both sides

\frac{2 m}{2} \neq = \frac{9}{2}

Divide the numbers

m \neq = \frac{9}{2}

\frac{- 10 m ^{3} \times 85 m ^{2} - 180 m}{2 m - 9} = 0, m \neq = \frac{9}{2}

Calculate

\frac{- 10 m ^{3} \times 85 m ^{2} - 180 m}{2 m - 9} = 0

Multiply

More Steps

Multiply the terms

- 10 m^{3} \times 85 m^{2}

Multiply the terms

- 850 m^{3} \times m^{2}

Multiply the terms with the same base by adding their exponents

- 850 m^{3 + 2}

Add the numbers

- 850 m^{5}

\frac{- 850 m ^{5} - 180 m}{2 m - 9} = 0

Cross multiply

- 850 m^{5} - 180 m = (2 m - 9) \times 0

Simplify the equation

- 850 m^{5} - 180 m = 0

Factor the expression

- 10 m (85 m^{4} + 18) = 0

Divide both sides

m (85 m^{4} + 18) = 0

Separate the equation into 2 possible cases

m = 0 85 m^{4} + 18 = 0

Solve the equation

More Steps

Evaluate

85 m^{4} + 18 = 0

Move the constant to the right-hand side and change its sign

85 m^{4} = 0 - 18

Removing 0 doesn't change the value,so remove it from the expression

85 m^{4} = - 18

Since the left-hand side is always positive or 0,and the right-hand side is always negative,the statement is false for any value of m

m \in / R

m = 0 m \in / R

Find the union

m = 0

Check if the solution is in the defined range

m = 0, m \neq = \frac{9}{2}

Solution

m = 0

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