Solve c7-(c^4:c^5)

Question

Simplify the expression

\frac{7 c ^{2} - 1}{c}

Evaluate

c \times 7 - (c^{4} \div c^{5})

Divide the terms

More Steps

Evaluate

c^{4} \div c^{5}

Rewrite the expression

\frac{c ^{4}}{c ^{5}}

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

\frac{1}{c ^{5 - 4}}

Reduce the fraction

\frac{1}{c}

c \times 7 - \frac{1}{c}

Use the commutative property to reorder the terms

7 c - \frac{1}{c}

Reduce fractions to a common denominator

\frac{7 c \times c}{c} - \frac{1}{c}

Write all numerators above the common denominator

\frac{7 c \times c - 1}{c}

Solution

\frac{7 c ^{2} - 1}{c}

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Find the excluded values

c = 0

Evaluate

c \times 7 - (c^{4} \div c^{5})

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

c^{5} = 0

Solution

c = 0

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Find the roots

c_{1} = - \frac{7}{7}, c_{2} = \frac{7}{7}

Alternative Form

c_{1} \approx - 0.377964, c_{2} \approx 0.377964

Evaluate

c \times 7 - (c^{4} \div c^{5})

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

c \times 7 - (c^{4} \div c^{5}) = 0

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

c \times 7 - (c^{4} \div c^{5}) = 0, c \neq = 0

Calculate

c \times 7 - (c^{4} \div c^{5}) = 0

Divide the terms

More Steps

Evaluate

c^{4} \div c^{5}

Rewrite the expression

\frac{c ^{4}}{c ^{5}}

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

\frac{1}{c ^{5 - 4}}

Reduce the fraction

\frac{1}{c}

c \times 7 - \frac{1}{c} = 0

Use the commutative property to reorder the terms

7 c - \frac{1}{c} = 0

Subtract the terms

More Steps

Simplify

7 c - \frac{1}{c}

Reduce fractions to a common denominator

\frac{7 c \times c}{c} - \frac{1}{c}

Write all numerators above the common denominator

\frac{7 c \times c - 1}{c}

Multiply the terms

\frac{7 c ^{2} - 1}{c}

\frac{7 c ^{2} - 1}{c} = 0

Cross multiply

7 c^{2} - 1 = c \times 0

Simplify the equation

7 c^{2} - 1 = 0

Move the constant to the right side

7 c^{2} = 1

Divide both sides

\frac{7 c ^{2}}{7} = \frac{1}{7}

Divide the numbers

c^{2} = \frac{1}{7}

Take the root of both sides of the equation and remember to use both positive and negative roots

c = \pm \frac{1}{7}

Simplify the expression

More Steps

Evaluate

\frac{1}{7}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{1}{7}

Simplify the radical expression

\frac{1}{7}

Multiply by the Conjugate

\frac{7}{7 \times 7}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{7}{7}

c = \pm \frac{7}{7}

Separate the equation into 2 possible cases

c = \frac{7}{7} c = - \frac{7}{7}

Check if the solution is in the defined range

c = \frac{7}{7} c = - \frac{7}{7}, c \neq = 0

Find the intersection of the solution and the defined range

c = \frac{7}{7} c = - \frac{7}{7}

Solution

c_{1} = - \frac{7}{7}, c_{2} = \frac{7}{7}

Alternative Form

c_{1} \approx - 0.377964, c_{2} \approx 0.377964

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