Algebra Examples

$\frac{m}{u^{2}} + r = - k - y$

Step 1

Subtract $r$ from both sides of the equation.

$\frac{m}{u^{2}} = - k - y - r$

Step 2

Find the LCD of the terms in the equation.

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Step 2.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$u^{2}, 1, 1, 1$

Step 2.2

The LCM of one and any expression is the expression.

$u^{2}$

Step 3

Multiply each term in $\frac{m}{u^{2}} = - k - y - r$ by $u^{2}$ to eliminate the fractions.

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Step 3.1

Multiply each term in $\frac{m}{u^{2}} = - k - y - r$ by $u^{2}$ .

$\frac{m}{u^{2}} u^{2} = - k u^{2} - y u^{2} - r u^{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $u^{2}$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{m}{u^{2}} u^{2} = - k u^{2} - y u^{2} - r u^{2}$

Step 3.2.1.2

Rewrite the expression.

$m = - k u^{2} - y u^{2} - r u^{2}$

Step 4

Solve the equation.

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Step 4.1

Rewrite the equation as $- k u^{2} - y u^{2} - r u^{2} = m$ .

$- k u^{2} - y u^{2} - r u^{2} = m$

Step 4.2

Factor $u^{2}$ out of $- k u^{2} - y u^{2} - r u^{2}$ .

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Step 4.2.1

Factor $u^{2}$ out of $- k u^{2}$ .

$u^{2} (- k) - y u^{2} - r u^{2} = m$

Step 4.2.2

Factor $u^{2}$ out of $- y u^{2}$ .

$u^{2} (- k) + u^{2} (- y) - r u^{2} = m$

Step 4.2.3

Factor $u^{2}$ out of $- r u^{2}$ .

$u^{2} (- k) + u^{2} (- y) + u^{2} (- r) = m$

Step 4.2.4

Factor $u^{2}$ out of $u^{2} (- k) + u^{2} (- y)$ .

$u^{2} (- k - y) + u^{2} (- r) = m$

Step 4.2.5

Factor $u^{2}$ out of $u^{2} (- k - y) + u^{2} (- r)$ .

$u^{2} (- k - y - r) = m$

Step 4.3

Divide each term in $u^{2} (- k - y - r) = m$ by $- k - y - r$ and simplify.

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Step 4.3.1

Divide each term in $u^{2} (- k - y - r) = m$ by $- k - y - r$ .

$\frac{u^{2} (- k - y - r)}{- k - y - r} = \frac{m}{- k - y - r}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $- k - y - r$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{u^{2} (- k - y - r)}{- k - y - r} = \frac{m}{- k - y - r}$

Step 4.3.2.1.2

Divide $u^{2}$ by $1$ .

$u^{2} = \frac{m}{- k - y - r}$

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Factor $- 1$ out of $- k$ .

$u^{2} = \frac{m}{- (k) - y - r}$

Step 4.3.3.2

Factor $- 1$ out of $- y$ .

$u^{2} = \frac{m}{- (k) - (y) - r}$

Step 4.3.3.3

Factor $- 1$ out of $- (k) - (y)$ .

$u^{2} = \frac{m}{- (k + y) - r}$

Step 4.3.3.4

Factor $- 1$ out of $- r$ .

$u^{2} = \frac{m}{- (k + y) - (r)}$

Step 4.3.3.5

Factor $- 1$ out of $- (k + y) - (r)$ .

$u^{2} = \frac{m}{- (k + y + r)}$

Step 4.3.3.6

Rewrite negatives.

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Step 4.3.3.6.1

Rewrite $- (k + y + r)$ as $- 1 (k + y + r)$ .

$u^{2} = \frac{m}{- 1 (k + y + r)}$

Step 4.3.3.6.2

Move the negative in front of the fraction.

$u^{2} = - \frac{m}{k + y + r}$

Step 4.4

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$u = \pm \sqrt{- \frac{m}{k + y + r}}$

Step 4.5

The complete solution is the result of both the positive and negative portions of the solution.

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Step 4.5.1

First, use the positive value of the $\pm$ to find the first solution.

$u = \sqrt{- \frac{m}{k + y + r}}$

Step 4.5.2

Next, use the negative value of the $\pm$ to find the second solution.

$u = - \sqrt{- \frac{m}{k + y + r}}$

Step 4.5.3

The complete solution is the result of both the positive and negative portions of the solution.

$u = \sqrt{- \frac{m}{k + y + r}}$

$u = - \sqrt{- \frac{m}{k + y + r}}$

$u = \sqrt{- \frac{m}{k + y + r}}$

$u = - \sqrt{- \frac{m}{k + y + r}}$

$u = \sqrt{- \frac{m}{k + y + r}}$

$u = - \sqrt{- \frac{m}{k + y + r}}$