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

Question

Simplify the expression

\frac{x + x ^{2}}{3}

Evaluate

2 x - \frac{x ^{2}}{3 x} \times (5 - x)

Divide the terms

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Evaluate

\frac{x ^{2}}{3 x}

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

\frac{x ^{2 - 1}}{3}

Reduce the fraction

\frac{x}{3}

2 x - \frac{x}{3} (5 - x)

Multiply the terms

2 x - \frac{x ( 5 - x )}{3}

Reduce fractions to a common denominator

\frac{2 x \times 3}{3} - \frac{x ( 5 - x )}{3}

Write all numerators above the common denominator

\frac{2 x \times 3 - x ( 5 - x )}{3}

Multiply the terms

\frac{6 x - x ( 5 - x )}{3}

Multiply the terms

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Evaluate

x (5 - x)

Apply the distributive property

x \times 5 - x \times x

Use the commutative property to reorder the terms

5 x - x \times x

Multiply the terms

5 x - x^{2}

\frac{6 x - ( 5 x - x ^{2} )}{3}

Solution

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Evaluate

6 x - (5 x - x^{2})

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

6 x - 5 x + x^{2}

Subtract the terms

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Evaluate

6 x - 5 x

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

(6 - 5) x

Subtract the numbers

x

x + x^{2}

\frac{x + x ^{2}}{3}

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Find the excluded values

x = 0

Evaluate

2 x - \frac{x ^{2}}{3 x} \times (5 - x)

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

3 x = 0

Solution

x = 0

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Find the roots

x = - 1

Evaluate

2 x - \frac{x ^{2}}{3 x} \times (5 - x)

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

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

Find the domain

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

Calculate

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

Divide the terms

More Steps

Evaluate

\frac{x ^{2}}{3 x}

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

\frac{x ^{2 - 1}}{3}

Reduce the fraction

\frac{x}{3}

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

Multiply the terms

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

Subtract the terms

More Steps

Simplify

2 x - \frac{x ( 5 - x )}{3}

Reduce fractions to a common denominator

\frac{2 x \times 3}{3} - \frac{x ( 5 - x )}{3}

Write all numerators above the common denominator

\frac{2 x \times 3 - x ( 5 - x )}{3}

Multiply the terms

\frac{6 x - x ( 5 - x )}{3}

Multiply the terms

More Steps

Evaluate

x (5 - x)

Apply the distributive property

x \times 5 - x \times x

Use the commutative property to reorder the terms

5 x - x \times x

Multiply the terms

5 x - x^{2}

\frac{6 x - ( 5 x - x ^{2} )}{3}

Subtract the terms

More Steps

Evaluate

6 x - (5 x - x^{2})

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

6 x - 5 x + x^{2}

Subtract the terms

x + x^{2}

\frac{x + x ^{2}}{3}

\frac{x + x ^{2}}{3} = 0

Simplify

x + x^{2} = 0

Factor the expression

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Evaluate

x + x^{2}

Rewrite the expression

x + x \times x

Factor out x from the expression

x (1 + x)

x (1 + x) = 0

When the product of factors equals 0,at least one factor is 0

x = 0 1 + x = 0

Solve the equation for x

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Evaluate

1 + x = 0

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

x = 0 - 1

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

x = - 1

x = 0 x = - 1

Check if the solution is in the defined range

x = 0 x = - 1, x \neq = 0

Solution

x = - 1

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