Solve (1)/((2v)/( 3 (1)/(2v)))-7

Question

Simplify the expression

\frac{3 - 28 v ^{2}}{4 v ^{2}}

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v = 0

Show Solution

v_{1} = - \frac{21}{14}, v_{2} = \frac{21}{14}

Alternative Form

v_{1} \approx - 0.327327, v_{2} \approx 0.327327

Evaluate

\frac{1}{\frac{2 v}{( 3 \times \frac{1}{2 v} )}} - 7

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

\frac{1}{\frac{2 v}{( 3 \times \frac{1}{2 v} )}} - 7 = 0

Find the domain

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\frac{1}{\frac{2 v}{( 3 \times \frac{1}{2 v} )}} - 7 = 0, v \neq = 0

Calculate

\frac{1}{\frac{2 v}{( 3 \times \frac{1}{2 v} )}} - 7 = 0

Multiply the terms

\frac{1}{\frac{2 v}{\frac{3}{2 v}}} - 7 = 0

Divide the terms

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\frac{1}{\frac{4 v ^{2}}{3}} - 7 = 0

Divide the terms

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\frac{3}{4 v ^{2}} - 7 = 0

Subtract the terms

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\frac{3 - 28 v ^{2}}{4 v ^{2}} = 0

Cross multiply

3 - 28 v^{2} = 4 v^{2} \times 0

Simplify the equation

3 - 28 v^{2} = 0

Rewrite the expression

- 28 v^{2} = - 3

Change the signs on both sides of the equation

28 v^{2} = 3

Divide both sides

\frac{28 v ^{2}}{28} = \frac{3}{28}

Divide the numbers

v^{2} = \frac{3}{28}

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

v = \pm \frac{3}{28}

Simplify the expression

More Steps

v = \pm \frac{21}{14}

Separate the equation into 2 possible cases

v = \frac{21}{14} v = - \frac{21}{14}

Check if the solution is in the defined range

v = \frac{21}{14} v = - \frac{21}{14}, v \neq = 0

Find the intersection of the solution and the defined range

v = \frac{21}{14} v = - \frac{21}{14}

Solution

v_{1} = - \frac{21}{14}, v_{2} = \frac{21}{14}

Alternative Form

v_{1} \approx - 0.327327, v_{2} \approx 0.327327

Show Solution